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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?

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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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Which Spinners?

Can you work out which spinners were used to generate the frequency charts?

Boy or Girl?

Age 14 to 16 Short Challenge Level:

A witch claims that she can predict whether your baby will be a boy or girl, and she charges £100 for this service.

If her prediction is wrong, she offers to return your £100 fee and pay you an extra £50 compensation for any distress that she may have caused.

Assuming she does not have any supernatural powers, can you explain whether she is likely to make a profit or loss after 100 clients have given birth? 

If you liked this problem, you might also like the article it appears in, Con Tricks
You can find more short problems, arranged by curriculum topic, in our short problems collection.