Question

A pair of fair dice is rolled and the sum of the numbers is noted. Determine the probability that one die resulted in a 5 given that the sum is 8.

Answer 1

Given that we only care about one die, this makes the problem much simpler. What numbers can the die we care about be?

I've never seen a negative die, or one with 0s. So this means that the highest the value can be is 7--since the other die has to be at least 1.

Similarly, the lowest it can be is 1, since the other die would have to be a 7.

It can take on all integer values between these numbers, too.

So, the possibilities are:

{1,2,3,4,5,6,7}

For a total of 7 objects. The probability of something we care about happening is the number of things we care about divided by the total number of things. There's only one 5, so the probability is 1/7.

Answer 2

It's 2/5 actually... not sure why