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  Probability (Number theory)

Probability

Next topic: probability. This probably won't come up on the test ... but just in case it does, you should know that the chance of anything happening, is equal to the number of ways it could happen divided by the total number of things -- good or bad -- that could happen in all.

A complicated probability problem is one where either of these two halves is hard to figure out. In this case, you’ll want to break things down according to these two rules:

  • “Or” is plus
  • “And” is times

So, for example:

What’s the chance of getting ten or more total when you throw two fair dice?

The way to solve this is to reframe it as: what’s the chance of getting a 10 OR an 11 OR a 12 when you throw two dice?

The answer will be the chance of getting a 10 PLUS the chance of getting an 11 PLUS the chance of getting a 12, because “or” is plus.

Now, what’s the chance of getting a 10? Well, that’s the chance of getting a 4 AND a 6 or a 5 AND a 5, or a 6 AND a 4.

The chance of getting any particular number is 1 out of 6, or ⅙, so the chance of getting a 4 AND a 6 is ⅙ TIMES ⅙, because “and” is “times”.

The chance of getting any particular combination therefore, is 1/36. Therefore the chance of getting 4 and 6, or 5 and 5, or 6 and 4, is 1/36 + 1/36 + 1/36, or 3/36.

Now use the same idea for the rest of the problem, and as long as you’re careful about your arithmetic, you’ll get the right answer every time.

In case you didn’t already know this, you’re gonna need a lot of paper for these problems, but they don’t give you a lot of space, so ...write small. No, seriously.

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