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Card Game (a Simple Version of Clock Patience)

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in one pile. What is the probability that you win?

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In a Box

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

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Chances Are

Which of these games would you play to give yourself the best possible chance of winning a prize?

Odd Dice

Age 14 to 16 Short Challenge Level:

Three fair, six-sided dice are numbered as follows:

A:  1, 1, 1, 2, 2, 2
B:  3, 3, 4, 4, 5, 5
C:  6, 7, 7, 8, 8, 8

The three dice are rolled once. What is the probability that the sum obtained is an odd number?

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