SOLUTION: A pair of dice is tossed. Find the probability that the sum on the 2 dice is 12, given that doubles are rolled.

Question 1101504: A pair of dice is tossed. Find the probability that the sum on the 2 dice is 12, given that doubles are rolled.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Conditional probability is a confusing topic for many students, me included.

Formally, conditional probability is defined as P(A|B) = P(A AND B)/P(B)

For your example, B is the event of rolling doubles and A is the event of rolling double sixes.

P(B) = P(doubles) = 6/36 = 1/6
P(A) = P(double sixes) = 1/36
and
P(A AND B) = P(double sixes) = 1/36

Then the conditional probability, formally, is

For most problems in conditional probability, the formula associated with conditional probability is awkward for me. I find it easier simply to think of the sample space.
Specifically for this problem, finding the probability of double sixes, given that doubles were rolled, means our sample space is only the outcomes in which doubles were rolled; and we want to know how many of those outcomes were double sixes.

Using that method, there are 6 outcomes that are doubles and only one which is double sixes; so the probability is 1/6.
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