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# Chances Are

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### Gambling at Monte Carlo

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Age 14 to 16

Challenge Level

Here are five competitions you could enter.

Which one offers you the best chance of winning?

- You win a prize if you flip a fair coin and get twelve heads in a row.
- Our gardener has ranked her seven favourite plants in order. If you rank them in the same order, you win.
- Choose the top 4 from 10 famous pictures and put them in the right order to win.
- Throw five fair dice and get five sixes to win the first prize.
- You throw four ten-sided dice and win first prize if you get four sixes.

Click here for a poster of this problem.

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

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?

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?