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

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?

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?

Chances Are

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.

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