Question: A pair of dice is rolled in a remote location and when you ask an honest observer whether at least one die came up six, this honest observer answers in the affirmative.
a) What is the probability that the sum of the numbers that came up on the two dice is seven, given the information provided by the honest observer?
b) Suppose that the honest observer tells us that at least one die came up five. What is the probability the sum of the numbers that came up on the dice is seven, given this information?