Question

What is the expected value of the sum of the numbers appearing on two fair dice when they are rolled given that the sum of these numbers is at least nine. That is, what is E(X|A) where X is the sum of the numbers appearing on the two dice and A is the event that X ≥ 9?

Answer 1

The answer is 10

Explanation:

Lets define the probability cluster for all possible outcomes of two dices below:

A={(3,6),(4,5),(5,4),(6,3),(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}

There are 10 possible outcomes of two dices under the condition.

To find the expected value of conditional probability. We need to multiply the possibility with the summed value of two dices:

E(X|A)=(4*9/10)+(3*10/10)+(2*11/10)+12/10=10