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About Probability

Date: 7 Jun 1995 13:59:34 -0400
From: cad 10
Subject: Probability


I am just wondering how probability works.  How is it specifically done?  

Patrick Bettencourt

Date: 7 Jun 1995 15:00:47 -0400
From: Heather Mateyak
Subject: Probability

Well, I will try to give you a few examples of some probability questions.

Probability questions that deal with games are usually most interesting to
me.  For example, say you're playing with a deck of cards with a friend.
Say he challenges you that if you draw an ace on your first pick, he will
have to buy you lunch the next day.  How good are your chances of winning?
Well, this is a probability question.  Since there are four aces in 52
cards, your chances of winning are 4/52, or 1/13.  So, the probability of
you're picking an ace is 1/13, whereas the probability of you not picking an
ace is 12/13.  The odds are against you, but it isn't completely unlikely.

Let's take a more complicated example.  Let's say you and your friend are
playing with two dice.  He gives you the same challenge, except this time,
he challenges you to roll two sixes.  The probability of rolling a six on
each die is 1/6, but how about both at the same time?  To figure the
probability out here, we have to multiply the probability of getting a six
on each die.  So, we have 1/6 x 1/6, and our probability for rolling two
sixes is 1/36.  Your chances are even worse here!

Another interesting thing probability can show you that is somewhat
practical is your chances of winning the lottery.  If you play one of those
3-digit lottery tickets where you have to guess the 3-digit number exactly,
your probability of winning is 1/1000.  You can figure this out by noting
that the probability of you're getting the first number right is 1/10.  The
probability of getting all three right is then 1/10 x 1/10 x 1/10.  Not too
good of a chance!  The 4-digit number is even harder!  Can you guess what
the probability of winning that lottery might be?  And even more amazing is
the tiny probability of winning those multi-million dollar lotteries.  That
would be a little trickier to figure out, but it is a slightly different
problem.  Say there are 70 numbers they pick from.  Your chances of getting
the first number right is 1/70.  But since one ball has been removed, your
chances of getting the second number right is 1/69.  If there are six
numbers picked, can you figure out what the probability of winning this
lottery is?  (Remember to multiply all of the individual probabilities
together... 1/70 x 1/69 x ...etc.)

The last thing I can tell you is that probability can be used in a lot of
more important things than games.  One area probability can be utilized is
in the area of genetics.  A monk, I believe his name was Mendel, realized
the use of probability in genetics sometime around 1000a.d. or 1200a.d.  I
can't exactly remember.  Probability in genetics is very interesting, and
can help you see once again how useful math can be!

Well, I hope this helps.  If I confused you anywhere, please write back.
This is my first time responding to Dr. Math questions.

Associated Topics:
Middle School Probability

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