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### SAT Probability Problems

```
Date: 11/12/96 at 19:00:38
From: mike
Subject: SAT Probability Questions

How do you do probability problems?  Do you take the whole
thing and divide it by the possible chances?
```

```
Date: 12/12/96 at 19:00:18
From: Doctor Daniel
Subject: Re: SAT Probability Questions

Hi Mike,

I'll give you an example of a short probability problem and show
you how it'd be solved.

Suppose you roll 2 dice.  What's the probability that the result is
more than 10?  The answer is 1/12.  Here's how to get it:

A result of more than 10 has to be either 11 or 12.  There are only
three ways the dice could have fallen to give these results: 6 and 5,
5 and 6, and 6 and 6.  (Where the first number is what happened on the
first die, and the second number is the second die.)

So there are three possible ways to get more than 10.  And there are
36 possible ways to roll two dice (that's 6 choices for the first and
6 for the second: 6 x 6 = 36).

So the overall chance of getting more than 10 is equal to:

no. of ways to get more than 10
------------------------------- ,
no. of ways to roll the dice

which is 3/36, which equals 1/12.

The general idea, then, is that you compute the number of ways that
what you want to happen can happen, and divide by the total number of
possible outcomes.  This only works, incidentally, when every outcome
is as likely as the next one; for example, it won't work with dice
that cheat.

Good luck on the test!

-Doctor Daniel,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

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