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Gambling at Monte Carlo

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

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?

Win or Lose?

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

Marbles and Bags

Age 14 to 16
Challenge Level

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags (it is not known from which bag). The marble is blue. What is the probability that it was removed from bag A?

Bag A



Bag B