What is the probability of rolling a number greater than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?
I'm going to solve this in this way - we know that there are
We're constrained that one die must be a 6 and the total must be equal to or greater than 8.
When die A is 6, die B can be 2-6 but can't be 1, so we have 5 acceptable results.
When die B is 6, die A can be 2-6 but can't be 1, so we have 5 more acceptable results.
Now note that we've just double counted the (6,6) result, so we take away 1 good result, and end up with 9 and a total probability of