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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?

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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?

Swapping Sweets

Age 14 to 16 Short Challenge Level:

Kate and Anna each have a bag that contains a red sweet, a blue sweet, a green sweet and a yellow sweet.

Without looking, Kate takes a sweet out of her bag and puts it into Anna’s bag. Then, without looking, Anna takes a sweet from her bag and puts it into Kate’s bag.

What is the probability that after this, each bag contains a red sweet, a blue sweet, a green sweet and a yellow sweet?


This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.