If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 5. The probability is

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Explanation:

Refer to the dice chart below. It represents all possible ways to roll two dice and sum up the face values.

According to the table, there are...

There are A+B+C+D = 1+2+3+4 = 10 instances where we get a sum between 2 and 5. The table shows 6*6 = 36 sums total. This means there are 36-10 = 26 sums where they are between 6 and 12, aka "the sum being greater than 5".

Those 26 sums are what we focus on. Out of those 26 items, four of them are sums of "9".

The probability we want is therefore 4/26 = 2/13