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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?

Connect Three

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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.