Welcome. This is the Education Committee in the Vermont House of Representatives on Thursday, January 13. We are continuing our conversation about the state of our schools, however, our students, our faculty, our staff and our communities. And what are the things you would like us to do and what would the things that you would please like us to please not do this year. And I am welcoming, first, Jane Nichols from the Vermont Principles Association. Welcome. Thank you very much, Chair Webb. Good morning, House Education Committee members. As Chair Webb said, I'm Jane Nichols, Executive Director of the Vermont Principles Association for the Record. Here to testify today about how schools are doing in relationship to COVID and how the year's gone so far. My testimony is similar to testimony I gave in October and testimony I recently gave to the Senate with some updates. So, first of all, I want to predicate that my testimony is based on meetings I've had with principals since July, and that's over 100 principles that I've talked to. So I broke it up into the same buckets, Kate, that you had us do in October. The first thing is how are the children, staff and families and I just want to say and I'll submit written testimony as well. Children on average based on principles comments are struggling. As you know, there's a lot of issues around self-regulation at all levels but particularly disturbing in the younger grades, lack of maturity, which all is understandable given the fact that kids have had two years of an unreal experience. All this makes academic teaching very difficult for teachers, obviously. It's a partnership to meet the mental health and social emotional needs of our students. We need to eliminate silos in Vermont. We're very good at creating silos. We need to get all committees working together mental health working along with education, DCF working along with mental health to make sure that we're providing all kids with what they need. In my written testimony, I cite three different statements and I give a couple of links. And the big takeaway from that is that the American Academy of Pediatrics has labeled the public health, the mental health crisis, that an actual crisis that is now a national emergency. And three medical groups including the American Academy of Pediatrics recently released a report on that which I have attached in my written testimony. And really disturbing to me is that suicide attempts have risen. The number of ER visits for suspected suicide attempts, for example, by 12 to 17 year old girls, rose by 51% from early 2019 to early 2021. And that's according to the CDC. So those are national numbers. It's something that we're all very aware of and very, very worried about. In terms of principles, as you know, they're facing unprecedented challenges. The work that they've had to do so far is not sustainable. We're hoping that the changes in contact tracing and some of the responsibilities will make that a little bit easier. Principles are very worried about is this going to become the new normal. And it's cost to me members we've had four or five principles leave this year in the year I've never seen that happen before. I'm not going to judge that are just saying I'm hanging out to June, but then I'm probably going to walk away. So I'm very concerned about that I know that's true with teachers as well. Families of course are all over the place as you might expect. You've all heard about the issues with masking and anti vaccine parents and board meetings. We've also had some frustration more on a day to day level related to contact tracing, especially in situations where schools have sent home kids who have no symptoms and appear to be perfectly healthy. And of course that is now changing with the with the changes to contact tracing, contact tracing, the lack of a real statewide comprehensive cohesive response and maybe a mandate from the state like this looks like and allowing different schools to have different versions has made it difficult. And again, we are hopeful that the change to contact tracing that was recently announced will make things easier operationally and take some burden off of schools while ensuring probably most importantly that more students can be at school in person every single day. I already talked about contact tracing in terms of what is working what it's not. There are major staffing shortages as I know you're aware, fewer no substitutes, not just teachers support staff bus drivers paraprofessionals custodians that are level worse than ever before anyone's memory. I recently pinned op ed and digger. I've been a response about that asking people to reach out to volunteer in their schools and helping their schools and I had a parent reach out to me and say, I tried to reach out to my school and volunteer and I wasn't allowed to, because of fingerprinting. And it took so long I couldn't couldn't make it work. So, even when people want to help and do the right thing sometimes there's roadblocks to get in the way. This shortage is an acute immediate problem. And I'm worried about long term shortages as fewer people are going into education related jobs for a variety of reasons that includes teachers and administrators. As you know there's been issues with transportation, especially in terms of staffing and in some cases we've had to cancel school because we could not get the kids to school, because we could have enough bus drivers and we've had to cancel a lot of extra activities as well. Most principals are not able to serve as instructional leaders this year. The vast majority of the time is spent on management functions and getting things covered principles talk about every morning for the first hour hour and a half, they're usually meeting with people to say alright who's going to cover Jim today because the gym teachers got COVID or is out because of contact tracing. This is working. As I mentioned earlier in the year is that many schools have adults that are really bonding together. They're in survival mode but they're really working hard to support each other and most importantly supporting all the kids. I do want to mention that the work done in the area of SCL, and I put community schools into that bucket and after school programs and other programs that we do on a day to day basis and schools has been very helpful. I can't actually because I talked to directors in other states and we're in a lot better shape than a lot of people are. And I want to mention we are not in recovery mode. It's important to realize that we're still in survival mode, and many educators don't feel value the pension thing last year really hit hard people are very worried about that. So it's time at the legislative level to step up and completely support public education. This means making sure education fund dollars are being used in an effective way. We need to support our public schools and make sure education funds are not siphoned away by any groups or schools that discriminate against some of our children. That's a big issue for all of our groups that to prospect. And in terms of requests for legislative action or non action in 2022. I'd ask you to support the VPA retirement bill concept that allow educators to come out of retirement for one year to feel hard to fill positions. To me it's an easy win to win win win proposition because they would pay into the retirement system. We need to support any federal or other efforts that allow for schools to have four year olds and school full day for early kindergarten with corresponding FTE for Ed funding purposes I know that's tied to the president's bill. We hope that sometime that build back better gets across the finish line, especially in terms of early childhood, we are working with our national organizations to try to support that. And support any legislation that will provide financial assistance to educators at work and more economically depressed schools. If they did agree to stand those positions for a set period of time. This could take the form of support paying off student loans or extra enumeration. It's very hard in our rural schools to keep people. They often have teachers for a couple years and those teachers leave for higher paying jobs 20 miles further. That's more towards urban suburban areas. Make sure the state pays for any PCB testing mitigation measures so this doesn't become a budget killer for local school districts. Make sure that any work on Act 173 stays true to the major goals of that legislation, more flexibility for schools to better support students major reduction paperwork, focusing on serving kids and developing comprehensive student support systems. If you're going to add any legislation that puts more pressure and stress on school boards, superintendents, principals, teachers and support staff. This is a requirement is constantly growing without the corresponding support so please don't add anything unless you're going to take other things off the plate of educators or you add something new that's going to actually help make it learn, make the work more attainable. Lastly, please don't pass any laws that will further increase the divide between the haves and have nots. We need to make sure our poorest least resource school districts have access to high quality qualified educators, not just the districts with the most resources. There are a couple of bills being contemplated that would take would have an adverse effect on our most vulnerable students in schools. Please look at education related bills in terms of impact on our students first and foremost. Thank you and I take any questions and I can stay till 11 to answer questions with the others as well. I have a quick question for you. I'm not sure if the bill has come through yet and Amanda maybe you could check on that to see if the bill that allows teachers to come out of retirement has been introduced. And in the meantime, Jay Nichols who do you think we would need to be hearing from I'm assuming we need to be hearing from the Treasurer's office. About impact on pension. Yes, yeah. But other than that, just the usual subs suspects. Yeah I think so and I think everybody's certainly in support conceptually the idea of the devil's all in the details, we need to make sure that if somebody comes out of retirement. They're paying into the system with the new money that they're getting and they're paying into the system at the highest rate just like they're a new teacher. They're really helping the pension fund. And at the same time, they're not taking help by losing their retirement, and they're filling a position that we are really that we're not able to fill. Amanda, can you put that on our list. I'm going to see if the bill has been introduced or not yet. And I want to get to that fairly fairly soon. Representative Austin. Yep. Hi Jay. Just, could you be a little bit more specific about the bills that are being proposed that would further to buy the halves and half knots. Well, I want you to look at that lens for every bill and I'm glad to talk about any of them but there's one bill right now that's in general military affairs. And that would allow teachers to essentially become free agents in terms of contracts. And so the way that that bill would work. And I testified against this a couple years ago it was put forth by representative Townsend if I remember right I think it's representative Townsend again this year. And she's trying to make sure that teachers have more opportunities to leave schools to go for other schools for jobs and I understand where she's coming from. But the point is that the way that it's set up is that if I'm a superintendent and our principal and we hire a teacher and she signs a contract in April to teach for the following year. She would be able to go right up to the first day of school and interview for other jobs and walk away. And that just leaves our most vulnerable students hanging in the lurch. So if we need to, we can come up with some type of a window as a hiring season or something along those lines that we have to what we don't want to have is teachers leaving at the last minute or very, very late in the school. Late in the school year and having to be very impossible to find qualified people to take their places in the following school year. So that's one of those bills where people have good intentions. And they're trying to support the adults, but they're really hurting the kids if they don't really think it through. Just let us know what that bill number is and we'll keep track we'll keep an eye on it. Okay, I can I'll have to email you I can't remember I almost feel like it's 80 but I could be wrong. Okay. Thank you to Austin. Are you excited. I'm done. Okay. Thank you. Thank you for that question. Representative common. Thanks and Kate you can shut me off if you want to postpone this discussion till the bill actually comes before us but in the, in the issue of bringing folks out of retirement to work, which seems like a great idea but I do wonder. I'm just going to run into issues with the NEA, who might fear that school districts would hire somebody coming out of retirement because they don't have to pay medical and other benefits, necessarily. Let's save that question I think it's a really good one when we get to the bill. Thank you. Thank you, Jay. I just want to ask. When you say you know it's time for the legislature to step up and do everything to support schools and teachers totally agree. Is there anything more specific it's kind of like parents I think wanting to go in and volunteer in schools right now. There's not necessarily anything we can do except do no harm but just want to ask, you know, is there anything else that more specifically we can be doing. I mean there's some things that we're going to come to you with but for example, we passed a law last year that said that public schools had to follow certain rules for an elementary for exclusionary discipline and private schools didn't have to. We've also passed laws before that has have allowed private schools to receive public funds that discriminate against our kids now that's something that hopefully we're all working on together. That's a huge issue for us. And it should be a huge issue for everybody if public education is a public good being paid for by the public taxpayers that we need to assure that no students are discriminated against and that includes religious schools or independent schools and we've got some great independent schools that do a wonderful job of including all students. And they get public funds and our argument is that any independent school that gets public funds needs to include all schools, our students in their school. Because that's the overall theme representative Brady. And some of that is, I believe some some some of that was addressed in the 2200 rule I believe. We're working on the 2200 rule we have a subcommittee. Yeah, Sue is on that subcommittee. As am I, the Maryland my husky and Milmore, a couple other different independent schools. And I think we're close to some resolution on the 2200 rules. Representative Brown. Thank you. Are you hearing so we heard some testimony yesterday from the Vermont School Nurses Association about the changes that are being made to contact tracing are you hearing from your school communities that those adjustments are going to help lighten the burden on school staff in terms of the work that needs to be done around contact tracing I'm still trying I think I'm still trying to understand what that shift in workload looks like and if it is going to help. Yeah, I think I testified about that a little bit in this committee. The other day, but maybe I was in Senate had talking about I had to remember and the answer is our executive council talked about it and we're basically going to go wait and see approach. We're optimistic that it that it will help we know that what we were doing before was not sustainable. There was no way. So we're hopeful that it's going to help there's some fear out there. We'll parents be honest those types of things that people you know we constantly worry about. Whenever I hear Dr Lee speak, it gives me some hope because he'll say even if somebody's not doing the right thing. As long as everybody else is masking appropriately taking mitigation strategies we're all so much safer. So, to answer your question directly we're hopeful principles are an executive counselor optimistic. So what we're going to have to wait see it plays out we got to make sure there's plenty of tasks and there's high quality mask in our schools and I think if we can do those two things, it can work. Thank you. And we are reaching out to the AOE following the testimony we got from the nurses association about contact tracing that what we heard yesterday seemed to be in conflict with what the agency said so we're reaching out to get some clarification from the agency on that. We're also reaching out to get more information on where we stand with masks and and testing from AHS and the AOE. Any other questions for the principles. We can move on to the special ed administrators and welcome Darren McIntyre. Thank you for joining us for the record could you just state your name and position. Thanks chair web and committee members. I'm Darren McIntyre executive director for Vermont Council special ed administrators. Similar to Jay and in terms of an update. What I submitted was very similar to testimony back in October. There were some updates and some others that I'll share verbally as part of the testimony today. As many have commented both yesterday and and even with Jay's testimony. We continue to see shortages. Our association is tracking those. We know statewide. There's some whereas in the neighborhood of 1300 vacancies across a variety of different positions. Specific to our association. I've tracked over 350. Those are a combination of special educators related service providers. SOPs behavior intervention as Paris school psychologist. All contributing to what many have mentioned. As a continued crisis with the shortage of staff. I've just recently. The information that I got from our membership. Over 30 of our members across 30 supervisory unions they've averaged the equivalent of 10 full time equivalent positions or 10 FTS for vacancies. That's led to the need for coverage of various roles. As Jay mentioned, you know, while that continues to be a challenge, I think one positive to that is it has helped with opportunities for collaborative teaming. And I think when Jay talked about some of the silos. There's a greater appreciation in many cases for the duties as others cover. In some cases, general ed for special ed special ed for general ed. As Jay mentioned, some of the administrators covering for teaching positions. So I've heard many say, I have so much more appreciation for the role. Hopefully, I think chair Webby mentioned yesterday. Hopefully, once some of this starts to improve, we can see opportunities for a reckoning and more collaborative teaming on these items. In addition to the shortages. We've seen more recently, an increase in special ed referrals. And I think that's paired with a number of different items. As folks have mentioned, just a strain on overall mental health needs for students in addition to staff on a student level, or seeing increased referrals for that reason. There's a significant regression because of continued absences. That has paired with increased special ed referrals. And I think related to upcoming rule changes in this conversation about delay or implement on July one. So I think there are several parent advocacy groups. Putting out information to parents and guardians saying, do the referral now to special ed. And if they're not eligible. Wait until after July one and refer again. We've created sort of increased anxiety and stress on an already challenging set of circumstances. Wanted to talk in terms of an update on that conversation of the implement or delay. And I think that discussion has no formal recommendation we continue to not have a consensus across our membership on that. That said, over 70% of our members continue to stress the need for a delay due to the various circumstances that we're talking about and the effects of the pandemic. So I think there's a contrast agreement with the intent of the law and the policy and want that to be heard to the committee. I think that has created sort of a level of irony where it's pushed many to say, we believe in the intent of Act 173 so strongly that we want to do it well. And that's a result field and needed pressure to delay. And I think Megan talked about many of the advantages and disadvantages that and her testimony yesterday, and her role as the chair of the subcommittee, reviewing some of the items related to that. Paired with what I just said, there's sort of a sense of if it goes into effect July one. We're almost going to see a reverse of the intent of the law with increased special ed referrals and increase in special ed service. And in many cases, you know, we've heard from Jeff and three of the superintendents yesterday and their testimony we know roughly 50% of the s us under that current waiting proposed formula and finance model 50% would probably have an advantage financially with that and the others would see a negative impact. And I think that in itself is also driving this conversation of if it goes into effect. It's roughly five months for guidance from AOE, and we're not. We're not seeing that in many cases. And, you know, I'm grateful and respectful for opportunities to collaborate and provide input from our membership with AOE and establishing expectations for those items but in many cases. Those are absent and void, and along with the shortages. There's that fear that there's just no opportunity for training come July one. So that in itself will lead to again potentially more referrals more financial impact of students on IEP's you know I guess I would add. In addition to that, we're continuing to collaborate with many of the key stakeholders around steps, regardless of whether there is an implementation or delay. We're trying to work with some of the, some of the districts that are further along and MTSS readiness and models for that. We want to be able to collaborate and scale those up whenever possible to help with preparation. Again, it's hard to do that if staff are covering all their duties and just no capacity for that. Chair Webb mentioned yesterday. Many of the special ed directors and le as had systems in place. Those were canceled. Some of the presenters themselves tested positive more able to engage other special education staff related personnel wouldn't have been able to participate so just the impact of a presence of staff. There's a need to cancel many of the trainings that would have been needed to implement. You know I think the other is steps to develop ways to mitigate the financial impact. And again testimony was provided yesterday on advantages disadvantages. Overall our members are saying we feel fairly confident that there's ways to mitigate over time the financial impact but the concern is we really need a delay because we can't recover from impact on educators and students well being loss of learning. So, again, the irony is, argues if the implementation is done well with 173 and these upcoming real changes around adverse effect and SLD identification, then there's going to be greater soon outcomes, instructional outcomes well being mental health related outcomes, systemic outcomes, and overall measures for tier one instruction and access for all students. But we're asking I guess ultimately for ways to support funding. It is going to go into effect for training. Some have existing methods through teacher master agreements where more formal training is needed and credit based coursework. So they're thinking of using idea be funds to support that, and not knowing, you know where things will go with financial impact for those 50 potential supervisor unions that may have. As we heard from john castle in north country, $2 million deficit. I'm not sure where training funds are going to come from, even if there are staff and and content available so support from the committee to find ways to fund financially, the training mentoring for all the items that we're talking about related to recruitment and retention with the shortage. And then, you know I heard, again, advantages and disadvantages of sort of phasing in potential delays, and I think the biggest impact, if we're moving forward with MTSS implementation and act 173 are the additional real changes around the risk of fact and as I'll do that on occasion so if there's a mechanism to slow that. I think it's going to compound the ability to do both at the same time. We would ask for considerations to be given around the timing of those. I'll stop there and see if there's questions. Thank you. Very helpful. Thank you so much for your response on 173. If I remember correctly, the, the adverse effect rule goes in July one. We might want to talk with a little more about that. Another time. Thank you. And we have any questions for the special administrators at this point. We time at the end also. Okay, seeing none. Jeff Francis. Welcome back. Good morning. Hello committee. Let me start with an audio check. Am I coming through okay. You're okay. Okay, if at any point I am not just signal me and I'll shut off the video. I do high speed internet with a mile of the state house, but still sometime experience problems. I'm going to suggest you turn it off now because it's just a little wobbly. Okay. Is that better. Yes. Okay. Thank you very much and I'll turn my camera back on for the questions if you have any. I'm going to start by thanking you for your leadership and commitment to delving into this issue. The challenges that have been brought to Vermont, the world, I guess the country and in this case specifically the education community are formidable. The testimony this morning is going, it's based on a meeting that two superintendent leaders, Jean Collins from Rutland Northeast, and Libby bone steel from Montpelio Roxbury had with the Senate Education Committee yesterday, excuse me last week. That testimony was a compilation of thoughts and considerations that we collected from a number of superintendents who serve on the VSA Board of Trustees. The first thing that those superintendents spoke about last week and I'll speak about this morning is just a high level of anxiety that's been brought to the education community by everything that's involved with the navigation of the pandemic. I think that you all are very familiar with that due to a combination of your own experiences and what you've heard from others. But we think that the nature and impact of the pandemic can't really be overstated. In many ways, the anxiety, anxiety levels are attributable to the experiences that people have positionally in terms of their own family, the school systems with it in which they work, the education system overall, and a lot of it has to do with the need to make changes in the communications around those changes. So at the beginning of last week, there was a high level of anxiety due to the return from school break. By the end of last week, we had information about the protocol changes that were being announced as we made the shift from Delta implications and impacts to Omicron implications and impacts. And everyone knows when we got back to work on Monday, there was a tremendous amount of anxiety, a lot of media coverage. In my mind, those manifestations are a product of the navigation of the pandemic, and really can't be attributed to, and I'm not saying that anybody is asserting this but sort of no will or bad actions on anybody's part. And yet there's a lot of energy around, you know, criticisms of the movement forward and so on and so forth. Now we're at a point where people have spoken more about the reasoning behind that change. And I think that the change is better understood, but a lot of the anxiety that was with us as a result of the pandemic persists. So the point there is that anxiety levels are high and are going to continue to be high. And we've got so many people on the front lines of this. You heard from the nurses yesterday, teachers in the classroom, family and children in their homes. But I think that collectively we're all hoping for some relief if Omicron does in fact run its course. But I think that for the time being the anxiety is with us and that's going to have profound effects. So that was one theme that we talked about last week and I'm speaking about today. Another theme is staffing capacity. And I know that you're fully aware of that I, I get examples every day in communications from school systems that either I'm directly the recipient of or that I'm copied on that just talk about the major implications of not enough staff. And as you know that affects school districts abilities to remain open and just has profound effects in the communities where staffing capacity results in the need to close the school or where shortages and staffing capacity cause people to, and this is literal, get no rest. So that's something else that that superintendents are talking about. And when I get to the recommendation section I'll refer back to it's, it's very, very challenging to have immediate solutions to any of these things but I do think that there can be a plan for thought process and there are going to be lessons learned out of this pandemic for mid and long term actions that we can take in order to address these issues. Both in the near immediate future and also over time. Student behavior, which is a recurring theme I think from all the witnesses and when I say student behavior. It's not an assertion that that it's a responsibility of the students that it really goes to their own existence within an unstable environment, which has been brought to us by the pandemic. And the superintendents who spoke last week in the Senate Education Committee took particular note and they have firsthand awareness of this and expertise I do not that in particular grades. It's being noticed more than others and the grades that they cited were kindergarten eighth grade and ninth and 10th grade, where they're seeing less stability than in typical years. And in the conveying those thoughts, superintendents indicated that schools don't have the capacity to deal with the dramatic increases in mental health and other behavioral needs. So that plays out in a number of ways including putting more pressure on the systems overall, but it should not be lost that the pressure that's being felt is being felt by by the students. So what is a very stable construct normally for kids with predictability and so on and so forth has become less so as a result of the pandemic. And thus the emphasis as we work through the covert navigation that we do everything we can to keep schools open in order to provide that stability but of course there's a contest there. Because there's also concerns about the well being of staff and what they've endured. There's no real solution here but it's an observation that's been made in the context of the current state of our schools. A point that I made when I testified back in October that's been reiterated is one thing that the General Assembly can do is to sharpen its awareness with regard to all of these things and I compliment you for the effort that you're putting into to doing that, both in the context of yourselves your communities, the state the General Assembly overall, but, but you know, the, the request that has been made for no new initiatives that will add burden or complexities is a very serious one. I think that that's well understood. In this committee, we know that the origins of legislation can come from any one of 180 legislators and to extent and you've signaled this this morning chair web that the House Education Committee can function as a gatekeeper to make sure that the that the very well benefited pieces of legislation that could add burden may not find their way to fruition in this general in this legislative session I think is deeply appreciated but as has been alluded to and stated directly by other witnesses. There's a bunch of things going on that need to be tended to that create a from a public policy standpoint. Big agenda in the category of unfinished work. You just spent 15 minutes talking with Darren about Act 173 we know how complicated that is at this juncture. We know that right this moment other committees in the State House or the virtual State House are working on the important matter of the waiting study which is a, I'd say it's a colossal public policy issue right now. I spent almost two hours yesterday, speaking with 40 plus facilities managers representatives of the Department of Health of the Agency of Education and the Department of Environmental Conservation talking about school facilities issues alone. Any one of those main topics could occupy all our time. And here we are treating them as, you know, not ancillary measures but measures that are taking time, even as we contend with all of the factors that that, as I said have been brought to us by the pandemic that have real influence and impact on the ground. So while I'm redundant in these messages I'm redundant because I don't think that what I'm saying can be stated strongly enough. We were also asked by the Senate Education Committee to talk with them about what we believe the General Assembly can do to be helpful. As I just completed first and foremost, we want to make sure that we have a light year legislatively, while turning into I think that the responsibilities that are already on the table. We agree with the VPA and others that the legislation that would allow retired educators to augment the education workforce should be treated as an imperative. Superintendent Collins, who spoke in the Senate Education Committee last week, talked about the fact that in one classroom in one grade in her school system. They've changed teachers three times and they're about to need to change for the fourth. And that's attributable to the fact that people currently have limited capacity to work if they're in a retirement status and want to come back. I don't know how much that's happening from school system to school system across the state, but in terms of the ability to temporarily provide relief to bring stability to school systems currently, if we could get a law enacted that would allow folks to return to work if they're retired without penalty. We do think that there's promise in terms of greater stability under that approach. I want to compliment the General Assembly for the very rapid action that it took around procedures for annual school district and town meetings. So the testimony that I'm referring to right now thematically was delivered on the first day of the session. And here we are just a little more than a week and a half later and the bill to address town meeting issues. It's on its way to the governor for signature if it hasn't been signed already. In that vein or category, I think you've probably either experienced or read in media accounts that there's been a period of time for school board members were conducting their meetings has been challenging because of COVID and other factors. But there's a bill that's being considered that would allow for remote operation of regular school board meetings without having to maintain a physical location to conduct those meetings entirely virtually. We support that that also looks like it will be received favorably by the General Assembly. I don't know what the status of that bill is today but that's something that was cited as being particularly useful. In terms of the worker shortage and this is a longer term need. We think a focus on and I know your committee has discussed it what measures can be taken to induce more stability in the delivery system by having more people interested in serving public education would also be helpful. And then finally in terms of the testimony that was offered last week. Thematically there was a big emphasis on mental health supports for children. And to the extent that there's an ability to focus on how we can enhance mental health supports for children both through the public education system and through designated agency and other measures. That's a need that is likely to persist for quite some time so from a system standpoint. And I know that you're focused on this in the past and are focused on it currently but that is really a necessary body of work. I'm going to wrap up here in a second and I'll answer questions. But I wanted to respond to the questions that were are being considered right now with regard to the changes in protocols with take home testing. As opposed to contract tracing and test to say. Initiatives in schools that the current transition as it were. And like the VPA superintendents are eager to see all the guidance with respect to that transition. I've heard Commissioner Levine and Secretary French talk about the rationale and also Dr. Lee about the rationale for the change. The rationale makes sense. I think that there is a the most important element of that transition other than the logistics is communicating the you know the the reasons why and how it will occur. But our association does rely on the experts in the public health field. We support those and logistically the changes that are made are being are being played out in public schools. And I think that's one of the reasons why schools have really risen to the occasion. They're being asked to rise to the occasion one more time so communicating the how and the why is extraordinarily important. And I would add just one point that I think is probably familiar to the committee. One of the things that we learned when we learned that guidance was that there may be some deemphasis on staff within schools in terms of their ability to obtain tests themselves and participating touch tasting in their lives. And what was referenced by superintendents is the fact that we need to make sure that we've got stability in the workforce by making sure that they are as well situated and I don't know any other term to use then comfortable as possible. And I think that even through the shifts that are going to take place operationally. We need to make sure that we're highly responsible to the workforce in terms of making them as confident as possible that they're that requires real clear explanations, understandings and access to resources that will provide that confidence that they are working in the safest possible environment. So with that, I will pause. I'll turn my camera back on and I'll answer questions, if you have any. I understand that you, you meet with the secretary on a fairly regular basis and help to speak with him about this guidance. Are you able to help in delivering the guidance so that it will be more accessible to the field to actually understand. You know complex times as complex communication is changing a lot. Everybody's anxiety is high just to help with the way the messages are delivered that obviously that the message is important but the delivery of the message is also important. Do you, are you able to provide him feedback. You know what I would say is, and I thought about this over the course of the last week. And as I've, as I said ad nauseum in my testimony this is extraordinarily challenging and there's nothing perfect about it. Secretary French communicates with individual superintendents on a daily basis with regard to challenges that come up in their systems. He also meets with superintendents every Thursday at two o'clock and sort of runs down what's transpiring. He prefaces those meetings by saying that what transpires verbally shouldn't be construed as written guidance. The guidance will be construed as the guidance the guidance will come in written form. And that's because the communicators and state government, you know they're operating in two directions they're communicating with the field but there's also a decision making apparatus and state government that they participate in. The answer your question is a qualified yes right so we're able to give the secretary feedback about, you know, our impressions and responses to what's happening. He's got another set of limitations and conditions that he needs to respond to. But the answer your question is yes, the other thing and I thought about this a lot over the last week to where we have now I think 117 school districts in Vermont. There are 51 supervisory unions there's those three independent tech center districts. You know, to the extent that we regard public education as an ecosystem as it were, every one of those districts and in some instances schools are ecosystems on their own. With, you know, different compliments of teacher, different socio economic and demographics of kids, different socio economic and demographics of communities. So, so part of the complication is, you know, the challenge of the pandemic overall but also how anything plays out in any given community. You know, I've taken too much time in a long winded response. So yes, we do have an opportunity to provide feedback. I think there are limitations, even with that feedback on how decisions get made. And a lot of this plays out community to community household to household it's it's you know it's the nature of, I think what a crisis is. So I've spoken too long on that but those are my thoughts on it. Okay, thank you very much. I'm aware of the time I want to see if there are any questions at this point.


Hey good morning guys. It's been a while since I've made a video about getting into PA school, but here we go. Here's a video about getting into PA school. And by the way, if you're new here, my name is Boris. I'm a board certified physician assistant. I've been out of PA school for about six months. I've been working, practicing as a physician assistant for about three months. And if you look back on my channel, you can see my whole story, how it took me 14 years from the time that I decided I wanted to practice medicine until I finally graduated with my PA license and actually started practicing medicine. So it was a really long road, really long journey, lots of mistakes, lots of ups and downs, lots of learning. And that's why I feel qualified to teach people how to get into PA school, especially if they're not the most competitive applicants. Okay. So just in case you're new here, that's what this channel used to be about. Kind of changing course right now. But anyway, I digress. The point is, this video is about getting into PA school. And what motivated me to make this video is a pre PA counseling session that I just did with a, I'd say probably middle of the road, pretty competitive applicant, definitely not someone with like a low GPA who really needs a lot of help, but definitely not like someone who's just a total shoe in to any school that they want to go to, someone kind of middle of the road. I would expect that this person would get in on their first try if they apply to enough schools. And if they apply to the right schools, so schools that are right for them, and maybe schools that they've made a personal connection with, like I've talked about in countless videos on my channel. So the title of today's video, the topic is focus on your strengths and focus on what makes you unique as an applicant when you're applying to PA school. So that means when you're answering questions in your interview, if you get an interview, when you're writing your essay, and when you're just crafting your Casper and choosing what to emphasize, what experiences to talk about, and what to talk about in those experiences. So for example, without giving too much detail away, this patient, this patient, I'm so used to talking about patients now and not students because I'm actually practicing, and I'm not in school anymore, so sorry, this student, this pre-PA student, this PA school applicant had a pretty good GPA definitely within the range that you would expect to get into PA school. They had a good amount of hours, patient care experience hours, and they were high quality, definitely in the thousands. And what was cool is that these hours were actually gotten doing something that the person was passionate about, not just some random medical job to get hours like scribing or CNA, unless you're really passionate about scribing or CNA, it wasn't something run-of-the-mill, it was something actually pretty unique and consistent with this person's interests, clinical interests. And so I thought that was very cool and actually pretty unique about this person. So the point is, this person had a good GPA, lots of hours. Those are like the twin pillars of getting into PA school, the main things. Now, a lot of the people that you compete with, most of the people actually that you compete with, are going to have those two things in check. They're going to have high GPAs, they're going to have plenty of high quality hours. So how do you stand out? How do you set yourself apart from all those people? Because not every single person with a high GPA and with a lot of patient care hours gets in. So how do you set yourself apart? Well, in this person's case, this person spoke like three or four languages, I forget, but more than two and like fluently. So three or four languages fluently, which is amazing. And then there was the thing that I just mentioned, where basically all of their hours or most of their hours were gotten, working in a field that they were actually very passionate about, and it was actually a very unique field of medicine. It was pretty niche. So you might think like, oh, a broad experience working at the ER, working in primary care might be the best. And you know, I could see the merits of that argument, but at the same time, working in something very unique and then wanting to practice in that area as a physician assistant, once you get certified, I think it's very interesting. And I think it's pretty rare in an applicant. So I thought those two things, the fact that they were trilingual or quadrilingual, like more than two fluently, and that they got a lot of experience in this very niche, very unique field. And they're very passionate about it. And they actually have experience in it going into school. And the fact that they actually want to work in this field after school, I thought those two things were very unique, definitely very cool. And something that this person can speak about very passionately in their interview, in their essay, and just all over their castbook. And one thing that I thought was kind of weird, actually, was this person didn't really talk about this a whole lot in their essay. And what this applicant actually told me was I didn't think it was important. I didn't think that it was that unique that I speak three or four languages. I didn't think it was very unique or very interesting that I actually want to focus.  Now, true, that might change. But the fact that this person is so set on this one field, I thought was really unique, was really cool. And at this point, since I've been doing these pre-PA counselings and editing people's essays and doing mock interviews and basically helping probably well over 100 people get into PA school at this point, I've seen a lot of applications. And I told her from my experience, and also just from talking to my classmates in school and just seeing lots and lots of practicing PAs and people going to PA school and people in PA school, I told her those two things were very unique and very, very, very, very valuable as a practicing physician assistant. So I told this person to absolutely focus their essay and if they get an interview to focus their interview answers on those two things. So what is the topic of this video? Focus on your strengths. Focus on what makes you unique. Those two things are extremely important. And if you are like this person and you have something like that that makes you stand out, that if you think critically about it, you know not every PA school applicant is going to have and most will not, those are things that you need to focus on. Does that mean that you don't also need a high GPA and plenty of high quality hours? No, no, those are like prerequisites, their minimums, everyone who gets in has to have those two things. But how do you set yourself apart and make yourself interesting and make yourself valuable to a PA school and eventually to an employer? Those are the things that make you unique. So think about those things and absolutely do not be afraid to emphasize them. In fact, emphasize them as much as possible. Okay, guys, that's all I have for today. If you want my help getting into PA school, I do still do that. I do still edit essays, do pre-PA counsellings, do mock interviews, just not very often anymore since I'm practicing and I just don't have a lot of time. So I do maybe one or two a week at most. So if you want me to help you, go to my website boristhepa.com, see how to book one of those services. If you have any simple questions you think I can just answer that you think people can get a benefit from, besides just you, leave it in a comment. I'll answer that and that way everybody gets the benefit of my answer. All right, guys, I'll see you in the next video. Thank you for watching.


Let's start. Is it recording? I think it is. Good. Lesson one says experimental and theoretical probability. It lists some objectives, but it's easier just to jump on in. It says visualize rolling a die. By the way, grammatically, one die, two dice. However, you're often going to hear me call this a dice because it's sort of become an idiomatic It's become proper in English, but technically a dice is wrong. It's like saying a car's or a truck's. It's one die. So most of the notes will be grammatically correct.  What's the theoretical probability of getting a five? What are the odds of getting a five? And all of us have a very, very basic, intuitive understanding of the odds. Probability.  And if you don't believe me, think about how superstitious, how horoscopes, how we try and read things into everything, we have a bad understanding of randomness. But the very basics we're pretty good at. What are the odds? Okay, I don't want to write out the theoretical probability of getting a five is one out. So here's our notation. First of all, for probability dill in its traditional, we use a capital letter p for the probability. Makes sense. And then we put a bracket and in the bracket, we write the condition that we're talking about. In this case, it's rolling a five. Close bracket is one out of six. I would read that out loud, Matt, not p bracket five, bracket equals one slash six. I would read this as probability of getting a five is one out of six. It's a good notation. Now, this is the theoretical probability. So theoretically, if I rolled the dice 300 times, how many fives should I get? Theoretically. Do the arithmetic? Try. 60, 50, 50. Okay.  Do you think if I actually did the experiment, I would get exactly 50? In fact, I'd be very suspicious if somebody told me that they got exactly 50. I'd be suspicious if they told me they got one. I'd probably, Miguel, take their word for it if they said they got anywhere between 40 and 60. I probably wouldn't but you know what, even if they said 25, I'd say prove it but it's possible. So theoretically, 50 out of 300, which reduces to one out of six versus experimental. Now, they want us to simulate rolling it and on your TI graphing calculators, some of you will have a probability simulator, we're not going to. We're just going to understand that the experimental would be different, probably. But here's what, oh, come on, mathematician begins with the letter L. Not fair, Matt. Is it? Maybe it is. One of the guys who initially wrote the first drafts of the mathematics behind probability and by the way, the earliest probability mathematics was done because a wealthy noble gambler had been interrupted in the middle of a game and he wanted to know what was the best mathematical way to split the pot because he was ahead but he hadn't won yet. So he was saying, should I get it all because I was ahead? So he wrote a letter to a mathematician named Fairmont and Fairmont in this letter back to him, basically developed most of probability mathematics. Anyhow, here's what Fairmont said. Now, this is our theoretical probability, 1 out of 6. He said, if you rolled 300 times, you might not get 50 out of 300. 1 out of 6. If you rolled 3,000 times, you would get closer to 1 out of 6. If you rolled 3 million times, you'd get even closer to 1 out of 6. In fact, he said that the more you do the experiment, the closer it approaches the theory. Good morning, sir. Again, we have a pretty good understanding. Example 2. Suppose one card is drawn from a deck of 52 cards and we drew a little 52 card list for you here so you can kind of visualize. You have four suits. You have how many cards in each suit? 13, 52 cards altogether. Okay, what's the probability that it is a face card? And I would write it as probability of f for face card. Well, the first rule of probability, Justine, and it's so obvious we're not going to write it down, the first rule is if you can count it, you can solve it. Face cards. I'm going to circle them with my pencil. Those are face cards.  And the other face cards are the jacks. The jacks. I can count it. How many face cards have I circled, Justine? 12 out of how many cards are there altogether? 52. Now, by the way, you're going to find most of the time the fractions will reduce. I never will. And I'm going to tell you not to, although they will reduce the fractions in the multiple choice answers, but we'll be using the fraction button very quickly on our graphing calculators because we're lazy. We want to be efficient. I prefer them not reduced because I'm going to tell you the odds are very good. If I wanted to do any kind of math with this, I'd want a common denominator of 52 anytime I'm dealing with cards anyways. And I just have to find a common denominator. I'll leave it like that. A red ace. Okay. Probability of red A. I'll circle those in red. What do you get? Four out of 52. Oh, Mr. Dewick, you did it wrong. Good gosh. You're right because it's the red ones. It's only these two, isn't it? How about two out of 52? Good gosh, Mr. Dewick. That was terrible. By the way, so again, visualize our deck of cards. You know, I should have a deck of cards in my hand for this. So suppose I shuffle this. What's the probability that if I reach in for a card, that it's a face card and a red ace at the same time? It's a trick question. Zero. And how can you tell from my little diagram there because nothing is overlapping in the circles? We're going to talk about what that means as well. We're going to be very important for us to understand whether something can happen at the same time or not. We're going to give that a special name. So here's the official mathematical definition of probability. It says, if there are n equally likely outcomes, 52 cards, and our outcomes are favorable to your event A, two red aces if that's your event, or 12 face cards if that's your event, then the theoretical probability of event A is it's the number of successful outcomes divided by the total number of outcomes. And that was how it was first defined. One of the first, one of the best tools I'm going to give you is a tree diagram. So here's a great question that very quickly tells you how bad our intuitive understanding of even basic probability is actually. What's the probability that in a family of three children, there are exactly two girls? In a family of three kids, there are exactly two girls. Now we are going to assume there's a 50-50 chance of when a child is born that it's a boy or a girl. I've been told that actually it's not quite, but it's something like 49.9999 and 50.00s. Anyways, we're going to assume it's 50-50. I need to double check that. Here's what I'd like you to do. So here's the question. What are the odds? What's the probability that if you know a family has three kids, exactly two of them are girls, I'd like you in the margin to write down what you think the answer might be right now. Best guess. What's your gut instinct? Write something down. What out of what? And then we're going to find the actual answer. And Stacey, the reason I'm doing this is I want you to get suspicious of your own gut instincts. If you don't think we have bad gut instincts, you've never been to Las Vegas.  Terrible. So here's how I would solve this.  Don't draw those in just yet. I'm going to put those right now. You'll draw those in afterwards. I'm going to use a leveled tree. I'm going to say for the first child, you could have a boy or a girl. Then you could have a boy or a girl, a boy or a girl, and then you could have a boy or a girl, a boy or a girl, a boy or a girl, a boy or a girl. Write that. And you don't necessarily have to put the levels there, but you know what? In our notes we will, so we know what the heck we did. We said here there are three events. First kid, second kid, third kid. So solution steps, it says draw tree diagram, represent the possible arrangements of boys and girls in a family of three. Each branch is equally likely, it says. Why? What are our assumptions? We're assuming the odds of having a boy or a girl are the same. Reasonable assumption. How many branches, once you've drawn this and you're going to get good enough at trees, they'll take you about one second, but they're so useful. How many branches, once you've drawn this out, contain exactly two girls? Let's see. This branch here has three boys. This branch here has one girl. Oh, here is a two girl branch. Are there any other branches that have exactly two girls? Here, here. Now you can use a highlighter if you want to, or if you don't have a highlighter, another thing that works great is putting check marks underneath. That one has three girls. Sorry, two girls. That one has two girls. That one has two girls. The probability of two girls is how many branches have I highlighted? How many branches have a check mark? Three out of how many branches were there? How many outcomes were there when we listed them all using a tree? Eight. Did anybody say that the odds were three out of eight? It's that eight you did? He's done some probability before. This guy, we've got to be careful. The rest of you though, if you're trying to do this intuitively, I defy you when you're told three girls, two girls, three kids, oh, and they're going to get a pop out of there. Yeah, it's two times, two times, two. It's the fundamental accounting principle. It's going to come back eventually. We're going to find better ways to do it, but very basic questions, surprising answer. In fact, most people might say, I suspect the most common answer, well, maybe two out of three or something like that. Trying to desperately do something with the numbers. Turn the page. Example four. When the pointer is spun twice, find the probability that you win a total of $10. How many times are we spinning the pointer? Twice. Generally, if there are two events, I'll use a tree. This one is going to be a bit of a bigger tree. It's going to have four possible outcomes. My tree is going to look like this. On the first spin, I can have a five, a 10, oh, hang on. Let's be organized, Mr. Dewick. A zero, a five, a zero, a five, a 10, or 20, and then I can have zero, five, 10, 20, zero, five, 10, 20, zero, five, 10, 20, zero, five, 10, 20. By the way, how many outcomes are there? How many possible outcomes are there? 16. Probability of $10 is. Now, I noticed for part B, I'm going to be reusing the same tree, so I'm not going to use a highlighter because that's really going to muck this up. You can, but I want to try and see if I can use this twice without redrawing it. I have a bit of a natural laziness. In this case, I'm going to go to checkmarks. You can't. It'll be fine. You might airy find it easier though just to quickly redraw the tree down here. Anyways, exactly $10, and I'll use green since I've used green over here. This one, this one, this one, oh, nothing over there. What are the odds of winning exactly $10? Three out of 16. Then we have probability of same number. Okay. That can be zero, zero, five, five, 10, 10, 20, 20, oh, four out of 16, four out of 16. We're going to also eventually find ways to do this without a tree. Specifically, when you have three or four events, it gets a bit ugly. We had three events here and even a three-level tree with two options already started to get a bit unwieldy by that third row. If we were spinning this pointer three times, how many outcomes would we have? Each one of these would have four more branches. I think 64, you know what? There comes the point when a tree breaks down, but we're going to do a lot of our initial probabilities with two or three nice events, and then we'll eventually try and generalize. Example five, two bills are randomly selected from the pot without replacement. You know what? That's a keyword. We're going to underline the word without replacement. Find the probability that you win a total of $10. Let's do our tree. On the first draw, we can get a zero, a five, a 10, or a 20, but now you're not replacing the bill. On this second draw, there's only three options. I've already picked a zero. What's left in this particular pot? Five, 10, and 20. Down this branch, there's also only three options. What's left? Zero, 10, and 20. Zero, five, and 20. Zero, five, 10. Right? How many outcomes are there this time? Not 16, yet four times three if you're trying to bring the fundamental counter-principle. Yes. Probability of $10 is, is it just two? Two out of 12. So there is lesson part one. So lesson two, part two, a bit more terminology, related events, and it gives us some objectives. So definition, the list of all the possible outcomes of an experiment is called the sample space. For example, when I flip a coin, what's the sample space? More specific, not two. What are they? When I flip a coin, what are the possible outcomes? What's the sample space? Heads or tails? Okay. When I roll a dice, what's the sample space? One, or two, or three, or four, or five, or six.   So part of the first thing you have to be able to do is figure out what can and what cannot happen. One bill, example one, one bill is randomly selected from this pot. What's the sample space? Traditionally, we use a capital letter S for sample space, equals. And traditionally, because it's a set, we use the fancy curvy set brackets, those ones. I won't take marks off if you don't, but I'll be proper. And the sample space here would be zero, five, and 10. And what is the probability that a $5 bill is selected? I don't think we need to do a tree for this one. We can do it intuitively. What is the probability that a $5 bill is selected? One out of three. Let's do a more interesting question. Example two, one bill is randomly selected from pot A and one is selected from pot B. So now we're picking from each, it says use a table to construct a sample space and use a tree diagram to construct a sample space. Which one is easier?  Generally, I use a table if there are two main samples. And there's more than three. Specifically, I use a table when I'm rolling two dice because it's six and six. If I did a tree, my tree would have 36 branches which is a bit of overkill. But both are acceptable. So if I was going to do a table, I would go like this. A and I would write a little zero, five, and 10 right there. And then I would write a little B. And just to the left of the first zero and below it, I would write a five, 10, and 20. And then I would draw a line like this so that I can sort of build my table. Can you see how this is going to look or going to work? It's going to go like this.  This is another way to list all of the outcomes in an organized manner. Oh, I can get a zero and a 10, a five, and a 10, a 10, and a 10. I can get a zero and a 20, a five, and a 20, a 10, and a 20. How many outcomes? Nine. I could also have done a tree. And this would be row A, zero, five, 10, row B, five, 10, 20, five, 10, 20, five, 10, 20. Which of those is easier to draw? I'm better at trees, but I'm going to tell you right now, if you're doing two dice and you will be doing two dice on your test as a classic question, table works way better because a 36-branch tree is overkill. Basically, I quickly use the fundamental counting principle to make a guess as to how many branches I'm going to have. It's less than 12, 12 or less. I'll probably go with a tree. What's the probability that some of the two bills is $10? So there's two ways I can get that. From my table, I could say, now they want the sum of the two bills. That means that it adds to 10. I could circle probability that sum equals 10 is what out of what? Two out of nine. Or from here, I would go, oh, they got to add to 10. Yay, no, yay, no, no, no, no. And there's my two out of nine as well. Example three. You're going to make it? No, nothing. One card is drawn from a well-shuffled deck of 52 cards. Use the graphical display from the sample space and find the probability of getting, okay. First of all, we want to find the probability of getting a red card. What I'm going to do is I'm going to circle all the red cards. I'm doing this for a reason. So if you have your pencil and you have different colors, great. Even if you don't, we're still going to circle and just keep track of things. Now, all the red cards are those ones and those ones because we're going to try to develop an equation shortly. What's the probability of getting a red card? 26 out of 52, which I know is one half, but I'm not going to reduce. Probability of getting a jack. So probability of a jack. So the jacks are those ones there. What's the probability of getting a jack four out of 52? What's the probability of not getting a jack? Okay, some terminology. Don't write this down. Here's what I don't want to write. That's dumb, waste of time. We have a better notation than that because so often in probability we want to find the odds of something not occurring. We have a special symbol for it. That's the probability of getting a jack. The symbol for not is if you draw a horizontal line above it. Write that down. That is the event not a jack. What is the probability of not getting a jack? Did you count the 48 cards? How did you get the 48? So this is going to give us another tool. I think what you went was 52, 55 Mr. Dewick. 52 out of 52 minus four out of 52. You went 52 take away four, yes? 48 out of 52. We call this using the complement. We say, you know what? Sometimes it's easier to find the odds of the opposite and then subtract from one if you really want to be fussy. What's the probability of a red jack? Can you see it from what we've circled? What we're really looking for here is the overlap. The overlap right there and that's why I went with this circling approach. How many red jacks are there? Two out of 52. Now compare that with the probability of red or jack. Now we need to define what or means in probability. Patrick you were late for class so you can have a detention at lunch or a detention after school. In English you understand in English the word or means one or the other but not both. In probability or means one or the other or both. In other words when it says a red card or a jack it also includes the red jacks and that's something kids often forget because the English meaning and the probability meaning are different. What it's really asking is how many cards are circled once or twice? I don't care. How many cards are red or jacks? Stop. How can I figure it out without counting them all? Could I go 26 plus 4? Why? In fact what I do is I go 26 plus 4 minus the overlap and that's going to give us next class our first probability formula. We're going to say if you ever want to find or it's the first one plus the second one minus any overlap because you've counted it twice. Anyways 26 plus 4 minus 28 yes. Circling things like this is a very good way to visualize stuff. In fact we use something called a Venn diagram. Charles Venn was a mathematician who honestly was not very good but one of the things he did in his notes is he popularized diagrams like this. They're named after him and it's one of the ironies because he really didn't knew much but Venn diagrams even non-MAT people often know what a Venn diagram is. It's a nice visual representation. So here is a Venn diagram. We would call this the event A. What would I call that there with the bar above it? The event not A and there is no overlap. You can't be A and not A at the same time. Sorry you can't. We call the event A not occurring the compliment and this is a word you're going to want to know. I'm even going to highlight it. It's a vocabulary word of event A and it's denoted by not A. It's sunny outside. What's the compliment of its sunny outside? It's not sunny outside. The Canucks won yesterday. What's the compliment of the Canucks winning yesterday? Not in the playoff game. What's the compliment of the Canucks winning yesterday? Canucks losing yesterday. You can't win and lose at the same time and the probability of something happening or something not happening has to add to 100%. Something either happens or it doesn't happen guaranteed every time or we can rewrite this. The probability of something not happening is one minus the probability of something happening. So let's go back to the Canucks yesterday. Okay. Over the regular season, let's suppose their winning percentage was 65%. So the probability of them winning any one game is 65%. What was the probability of them losing yesterday? B. 35%, 0.3%. A and B. So the event that both A and B occur at the same time is denoted by A and B and an event diagram, it's the overlap. That there is how I represent A and B. A or B. The event that A or B occurs or both is denoted by A or B and A or B is this or the overlap or that. This section right here is A only. This section over here is B only. This section over here is both. All of them together are A or B. What would this white section out here be? A or B. No. Was that a phone? No. Was that your alarm to wake up normally on days like, oh, we're going to talk. We're going to talk. Example four.  And this is where if I was doing a two dice question, I would quickly go one, two, three, four, five, six. One, two, three, four, five, six. I would draw a line, draw a line, and in 15 seconds or less, I can list all of the outcomes. There's 36 of them. It really doesn't take much time, go systematic. I've done that for you. So we have two events. Event A is the sum of the two dice is at least nine.  Because I can do color, I'm going to call this one blue, and I'm going to go with this one red. You guys are fine without color, but if you have color, pick a couple of colors. It says use the sample space in the table to find the following probabilities. Event A, probability of A. What was event A, Ian? Read it to me. What was event A? Read it out loud to me now that you're back with me. What I'm going to do is I'm going to circle any dice that add to nine or more. Here, here, here, here, because nine is at least nine. Oh, in fact, I'm spotting a bit of a pattern. It's this bottom corner, isn't it? Everything in that bottom corner adds to at least nine, which is also one of the nice things about a table. Often you'll find there's convenient patterns like that. How many did we circle? What is the probability? Oh, you know what, it's going to be out of 36. I can tell you that. What's the probability that two dice add to at least nine?  Let's see. So I think something like this, that one, that one, that one. Oh, I'm spotting a pattern here too, that one and that one. What's the probability of B? Five out of 36. What's the probability of A and B at the same time? Can you see it? What's the overlap? Two out of 36. What's the probability of A or B? How many are one or the other or both? You know what, how many are circled? 10 plus 5 minus 2, 13. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 13, if we count them by hand, the shortcut is add them up, but subtract the overlap because you've counted it twice. 13 out of 52. Out of 52, out of 36. Good gosh, I'm doing card questions. As soon as I wrote that, 13. What's the probability of not A without counting, please? 26 out of 36. In English, what does the event not A represent? Well, Ian, can you read to me the event A again? So in English, what does not A represent? I think it represents the sum of the two dice is, Troy, less than 9. So dealing for two dice, I quickly draw a sample space. You could do a tree, 36 branches is yucky. You could. You'd go 1, 2, 3, 4, 5, 6, 1, 3, 5, 6, 1, 3, 5, 6, forget it. Here is the lovely bend diagram. I don't know what the event is. I really don't care. They put dots to symbolize how many of each appear in each section. So there are 13 total outcomes and they're all equally likely. We've included that phrase in most of these questions. In a couple of days, we're going to ask, what if they're not equally likely? We can tweak it and adjust it, no problem. But for now, we're going to assume every event, every outcome has the same odds of occurring. What's the probability of A? I'll give you a hint. It's out of 13. I'm going to give you another hint. Don't say 3 out of 13 because it's not. What? Yeah, there are four circles in oval A. Four out of 13. What's the probability of B? Five out of 13. What's the probability of not A without counting, preferably? 9 out of 13. If it's 4 out of 13, 8, 9 out of 13, right? You can count, but let's use the complement when we can. It's always nice to use complements. What's the probability of not B? 8 out of 13. Okay. What's the probability of A and B occurring at the same time? You see it? 1, right? There's only one overlap. What's the probability of A or B? Now, there's two ways to get it. I can count 1, 3, 4, 5, 8, or I could go A plus B minus the overlap. Either of those works just fine. Here, I would almost certainly just in count because it's like a lovely diagram. Still, 8 out of 13. What's the probability of not A and B? 12 out of 13. And what that's really saying is what's not overlapping? What's the probability of not A or B? Now, I can get it from the complement here. 3, 5. Oh, those guys are not A or B or both. So far so good. Can you open your workbook please if you would be so kind as to page 400 and 26? I need to look at lesson 1 and see what I technically assigned the end of the lesson. 3 to 4. Sure, 3 is good. 4 is good. I said try number 6. Let's see. Tree diagram. Three people, but it's just so it's going to be a three level tree, but it's flipping a coin. So two outcomes. In fact, it's going to look almost the same as the boy-girl tree that we did at the very, very beginning. So 6 is okay. 7, yep. I'm going to assign 8 because we've done, by the way, if the probability of X is 0.2, what is the probability of not X in your heads right now? What is it? Yeah, the answer is D. Okay, we just did 8 anyways. And 9. So 9, you're going to have a two level tree. Box A, red, blue, yellow. Box B, red, blue, yellow, green. Draw your tree and then which branches have the same color? So number 9 is good. And then what did I assign on lesson 2? Number 8, which I already assigned. Okay, I'm going to add 10 and 11 and I'm going to hit stop here.


The final phase of the plan to concession the terminals of the country's four major international airports has begun. The Muratala Mohamed Airport in Lagos, the Namdiya Zikui Airport in Abuja, the Pothakot and the Malam Amino International Airport, Kaduna are affected by the new policy and amid fears by airport workers, the Minister of Aviation Hadi Silica has promised that no job will be lost to the concession arrangement. He also assured that there would be full negotiation with workers before the full implementation of the program. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


In the last week of 2004, Manasunami devastated coastal areas in Indonesia, Sri Lanka, Thailand, Malaysia and India, taking the lives of 200,000 people and destroying millions of homes. In order to avoid duplication of relief efforts and for better coordination among various countries, India, along with US, Australia and Japan formed a core group in the initial days after the tsunami. Later, the task was taken up by the United Nations. Unfortunately, the Indian subcontinent was to witness another huge natural calamity within a year of the tsunami, an earthquake of the magnitude of 7.4 on Richter scale with epicenter near Muzaffarabad in Pakistan occupied Kashmir POK struck in the morning of October 8, 2005 and devastated areas in Jammu and Kashmir, Pakistan occupied Kashmir and northern Pakistan. Entire villages and communities were destroyed. In Jammu and Kashmir, within 30 minutes of the earthquake, Indian Army and Air Force had swung into operation for providing relief in the worst affected areas of Barhmula, Ponch, Kupwala, Srinagar, Tangdhar and Uri in coordination with the state administration and para-military forces. While India's immediate relief effort concentrated on the Indian side of the line of control, LOC, it was conscious of the enormous tragedy that had unfolded on the other side. Among the first calls that President Musharraf received was from the Indian Prime Minister, Dr. Manmohan Singh, offering any assistance which Pakistan deemed appropriate. The Indian offer of help was neither a fad nor fetish, nor was it to play politics. It was based on purely humanitarian concerns, the considerations of insanyat. India firmly believed that it had the resources and the expertise to provide relief not only on its own side of LOC but also on the other side. On November 17, India sent the third relief train carrying 600 tons of relief material. This brought the total relief sent by India through one aircraft and three trains to about 900 tons of relief material valued at approximately 4.7 million US dollars. Due to tough terrain and destruction, many affected villagers on the LOC were inaccessible from the Pakistani side. India offered to mobilize relief supplies across the LOC and to even send foot patrols of medical personnel across. Following the initiative of the government, India's civil society institutions could not be left behind. Indian private sector companies, religious institutions, political parties, industry chambers and even private individuals sent aid to Pakistan. To facilitate the receiving of donations from Indian civil society, Pakistan High Commission in New Delhi was given permission to open a bank account to receive cash donations. On October 16, after government of India had already sent two consignments of relief material to Pakistan, the Delhi Sikh Curudwara Prabhanda Committee, SGPC, sent its first consignment of 18,000 blankets, 1500 tents and 20,000 meters of plastic sheets, bamboos and ropes to the Pakistan Sikh Curudwara Prabhanda Committee. The tsunami and the earthquake in two extremities of South Asia have brought to the fore the terrible consequences of natural disasters. It has taught us that no one rich or poor, India or Pakistan is immune to the wrath of nature. It has also hopefully taught us that the only power that can work in such circumstances is that of human fellowship and sharing without regard to national frontiers or ideologies.