how do I solve this probability Dice problem?

There is 1 way to get a roll of twelve:

6+6 = 12

There are 36 possible outcomes of two dice (6*6 = 36)

So the probability of rolling a sum of twelve is:1/36

The opposite probability is NOT rolling a sum of twelve and that can be found two ways.

1) You could count all the ways to not get a sum of twelve. Since there are 36 ways to roll the dice and only 1 is a roll of twelve, that means there are 35 that are NOT a sum of twelve. So the probability of NOT getting a sum of twelve is 35/36.

2) For any opposite probability you can subtract from 1.

P(not A) = 1 - P(A)

So just subtract the probability from 1:

1 - 1/36 = 35/36

Answer:

35/36

This is a fundamental concept, so let me give you a few more examples:

If the probability of it raining is 0.10, the probability of it NOT raining is 0.90.

If the probability of drawing an Ace is 1/13, the probability of NOT drawing an Ace is 12/13.

Remember the second rule, and practice some other examples.

1 – 1/36 = 35/36

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