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Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Whilst he was there he had an opportunity to bet on the outcome of rolling dice. He was offered the same odds for each of the following outcomes: At least 1 six with 6 dice. At least 2 sixes with 12 dice. At least 3 sixes with 18 dice.

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Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

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Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

Like Father Like Son

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

By "completely" we mean a son which has both his grandfather's eyes and his hair. Based on this fact, can you now guess Bob's hair colour and genotype? How can Bob be absolutely sure that he can't have an auburn son?

On the other hand, Alice has hopes having a daughter not looking like herself, but like her mother. But since Alice is brown - eyed, what does this mean about her mother? What can we conclude about the genotype of Alice?