Hello and welcome to the session. I am Deepika here. Let's discuss a question which says of the students in a college it is known that 60% reside in hostel and 40% are day scholars. Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year one student is chosen at random from the college and he has an A grade. What is the probability that the student is a hostler? Now in this question we will use Bayes theorem. So according to this theorem if even E2 so on EN are N non-empty events which constitute a partition of sample space S that is even E2 so on EN are pairwise disjoint and even union E2 union so on union EN is equal to S and A is any event of non-zero probability then probability of EI upon A is equal to probability of EI into probability of A upon EI over sigma probability of EJ into probability of A upon EJ J varying from 1 to N for any I 1 to N. So this is the key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution. Now according to the given question of the students in a college it is known that 60% reside in hostel and 40% are the scholars. So let even be the event that the students reside in hostel E2 be the event that the student is a day scholar. Therefore probability of E1 is equal to 60% which is equal to 60 over 100 and this is again equal to 0.6 and probability of E2 is equal to 40% and this is equal to 40 over 100 and this is again equal to 0.4. Now again according to the given question previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in the annual examination. So let A be the event of getting A grade. So probability of A upon E1 is equal to probability that the student getting an A grade is a hostel and this is equal to 30% which is equal to 0.3. Now probability of A upon E2 probability that the student getting an A grade is a day scholar and this is equal to 20% which is equal to 0.2. Now again according to the question at the end of the year one student is chosen at random from the college and he has an A grade we have to find the probability that the student is a hostel. So the probability that the hostel is getting an A grade and this is given by probability of even upon A so by using this term we have probability of even upon A is equal to that is the probability of the even even given that even A has occurred is equal to probability of even into probability of A upon E1 over probability of even into probability of A upon E1 plus probability of E2 into probability of A upon E2. Now we have probability of even is equal to 0.6 probability of E2 is equal to 0.4 probability of A upon even is equal to 0.3 and probability of A upon E2 is equal to 0.2. So on substituting these values we have probability of even upon upon A is equal to 0.6 into 0.3 over 0.6 into 0.3 plus 0.4 into 0.2 and this is equal to 0.18 over 0.18 plus 0.08 and this is again equal to 0.18 over 0.26 this is again equal to 18 over 0.26 which is equal to 9 over 13 so the probability that the hostel is getting an A grade is 9 over 13. So this completes our session I hope the solution is clear to you by and have a nice day.


Here's a seemingly boring plug and a plug point, something that we see every day, right? But here's an interesting question. If you looked at your plug carefully, you'll see that the top of the top pin is usually longer and thicker compared to the other two pins. Why do you think that is the case? Turns out that this can save us from deadly shocks. But how, you may be wondering, how can a little feature like making one pin longer can save us from shocks? Well, to answer that question, we need to explore what are the different wires that come to your plug point and what each wire does. So that's what we'll do in this video. We'll explore these three wires and then hopefully we'll be able to answer the original question. So let's begin. A wire that comes from one of these bottom holes, one of the wires will be insulated with red color and the other one would be insulated with a black color. The red wire is often called the live wire. So this is live or it's also called the hot wire and we'll see in a while why it's called that way. And the black wire is often called the neutral wire. So the immediate question could be why are they having different colors and why are they named differently? What's the difference between the two wires? Well, when I first learned this, I thought that one of the wires brings the electricity to our house and the other wire, the black wire will take the electricity back. And so this is how I should think. Electricity comes from say the electric poles to our house through the live wire and it goes back through the neutral wire. Simple, right? But that doesn't make sense mainly because we're not dealing with one directional current. You remember that we're dealing with alternating current, the current which keeps changing its direction once the current flows like this, then the current flows this way. So it doesn't make sense to say one wire brings in electricity another wire brings out electricity because the electric current keeps on changing its direction. So again, what's the difference between these two wires? Well, it turns out it's got something to do with voltage. If you look at this black wire, its voltage is always maintained very close to the voltage of the ground. And we'll see in a second what this really means, okay? And that voltage is often taken to be zero. And if you look at this live wire, it has a very high voltage. So this has high voltage. And the voltage difference between these two wires in India is often around 220 volt. If you're wondering why this particular number, it's got something to do with history and Edison and light bulbs and cost, we'll not get into that, okay? Don't worry about why it is 220, it just happens to be 220 for India. But again, what does that even mean? Well, that means if the current is flowing, say in this direction, then this wire must be having a higher voltage compared to the ground. We usually call that as the positive voltage. But then when the current is flowing in the opposite direction, then this should have a higher voltage, right? But its voltage remains the same. Now the voltage of the wire becomes less than zero. It can become negative. And that's when we'll have negative voltage. So the voltage of the live wire swings between positive voltage and negative voltage, making the current alternate. But the voltage of the neutral wire remains pretty much the same. And we can imagine this to be similar to a slide, one end of which is connected to the ground, other end is free to move up and down. So when the other end is up, notice the ball goes to the right this way. And now if I move this end down, the ball comes back. So by moving that end up and down, notice above the ground, below the ground, I can move the ball back and forth, back and forth. So this end is like the live wire. Its voltage keeps going above the ground and below the ground, back and forth, making the current go back and forth. On the other hand, the other end is like the neutral wire. It's always having the same voltage as that of the ground. Does that make sense? So what does that mean now? This means that if, let's say, a cat comes and touches this neutral wire, and let's say the insulation is broken, right? Then what's gonna happen to that cat? Well, over here the voltage is zero. Let me use white. Over here the voltage is zero. Even at the ground, the voltage is zero. Since the voltage of this is the same as that of the ground, there is no potential difference coming across the cat. And as a result, there'll be no current flowing through the cat. So the cat will not get a shock. But what if that same cat were to go and touch the live wire? Can you guess what's gonna happen? The cat is gonna have a very shocking experience because now notice the live wire is either having a much positive voltage compared to the ground or much negative voltage compared to the ground, compared to the neutral, compared to the ground. And as a result, in either cases, charges will flow between the wire and the earth, resulting in the cat getting a nasty shock. And that's why that wire is called live or hot wire, saying that it's an extremely dangerous wire, do not touch that wire. Now don't worry, no cats were harmed in the making of this video. Now of course, this does not mean you go and touch the neutral wires, definitely not, because this is in the perfect world. In reality, the voltage may not be exactly equal to that of the ground, so you might still get a shock. There can be faults and everything, so it's always dangerous to play or touch these wires. I recommend not doing that at all. But in short, the live wire is at a very high voltage compared to the ground, but the neutral wire has voltage very close to that of the ground. Okay, if the two wires are enough to provide electricity, why do we need a third pin, right? To answer that question, let's attach something to this plug point. Let's attach a microwave, let's say. If you could look inside this wire, you would see something very similar. You would see two wires, one connected to the live, which is red, one connected to the neutral, and the current flows back and forth between these two, and this is the internal circuit of that microwave, which I've just shown as a resistor over here.  Then why do we need a third wire? That is in case of a fault. Imagine when this microwave was installed in your home, some mishandling happened, and let's say the insulation of the live wire broke off and it started touching the metallic keys, let's say. So here's the situation. Let me zoom in. So you can see the insulation has come off, and the live wire is now touching the metallic keys. Now, again, let's bring back our kitty. She's gonna have a bad day today. If I switch on the plug now, what do you think is gonna happen? Well, because the live wire is touching the metallic keys and metal is a conductor, electricity will start flowing through the metallic keys, through the cat and into the ground, again giving our cat a very, very nasty shock. That is extremely bad. We want to avoid that. How do we do it? That's where a third wire comes into place. There will be a third wire, which is usually green in color, which is directly connected to the metallic body, and it goes all the way to the plug, comes out of the third pin. Again, let's zoom out. Comes out of the third pin. And then where does this wire go, you know? Let me get rid of that basketball. All right. And you know where that goes? That wire eventually comes out of your house and eventually is put inside the ground. And so this third wire is often called, no surprise, ground wire. This is the ground wire or the earth wire. It can also be called the earth wire. So how does that help? Well, now instead of the electricity flowing through the cat, that electricity will flow through this ground wire and go directly into the earth. Why? Why will it go through the wire and not through the cat? Because the wire has a much smaller resistance. This entire path has much smaller resistance compared to the cat. And you might know already that electricity tends to flow through the smaller resistance path. So almost all the electric current will flow through that path, ensuring the safety of our kitty. So in short, if there is any current leaking due to any fault, the ground wire ensures that we don't get electrocuted. At this point, you might say, wait, wait, wait. A quick thing, not all the plug points have a three pin, right? For example, mobile chargers and say, my MacBook charger, I have only two pins. What's going on there? Well, that just means that the amount of current we are dealing with over there is so miniscule that even if we get a shock, it's not a big deal. So it's not worth investing in putting another pin. In fact, my MacBook does give me a shock every time it's charging. It's not a big deal, all right? So only when we're dealing with high currents, high power devices, that's when the third pin becomes super important. So with that, let's come back to the original question. Why is the top pin, which we now know as the ground pin, why is that always longer and thicker than the other pins? Can you pause and think about this? Well, if the ground pin is longer, that means when you're inserting, it's the ground pin that gets connected first, meaning our device is made safe first. And only then that these two pins get connected, meaning only then the current starts running through this device to ensure that we will not get electrocuted in any case. And similarly, when you are removing the plug, again, we're ensuring that the ground is the last one to get disconnected. So we first disconnect the electricity from the device and then we disconnect the safety, the ground wire. Ingenious, right? And of course, the ground pin is also made thicker to ensure that we connect the plug in the proper position. This way, there is no chance that the ground pin will get inserted into the live hole, which can again cause problems. Anyways, that's it for this video. So let's see if we can quickly recall the important things. Do you remember what are the names of these three wires? Then, can you recall what is the voltage difference between these two wires in India? With that, try explaining to your friends or your family, why is it dangerous, more dangerous to touch the red wire compared to the black wire? What's the difference between them? And also, how does the green wire ensure safety? And with that, try explaining to your friends why in the three pin, one of the pin is always longer than the other two. If you have any difficulty answering any of these questions, no worries, just go back and watch that part of the video.