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A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

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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?

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?

Thank Your Lucky Stars

Age 14 to 16
Challenge Level

This problem offers an interesting context in which to think about permutations in a systematic way.

It can lead to an appreciation of Pascal's triangle.

There is an Excel spreadsheet available to download here where you can experiment with this problem.