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Three men are lined up behind each other

Three men are lined up behind each other. The tallest man is in the back and can see the heads of the two in front of him; the middle man can see the one man in front of him; the man in front can’t see anyone. They are blindfolded and hats are placed on their heads, picked from three black hats and two white hats. The extra two hats are hidden and the blindfolds removed. The tallest man is asked if he knows what color hat he’s wearing; he doesn’t. The middle man is asked if he knows; he doesn’t. But the man in front, who can’t see anyone, says he knows. How does he know, and what color hat is he wearing?

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Average: 8 (1 vote)

There are three bags

There are three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. You pick a random bag and take out one marble, which is white. What is the probability that the remaining marble from the same bag is also white?

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Average: 8 (1 vote)