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Gambling at Monte Carlo

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

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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?

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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?

Thank Your Lucky Stars

Age 14 to 16 Challenge Level:

A star is placed in the bottom right hand corner of a grid. You toss a coin and

  • if it is heads you move the star one square up
  • if it is tails you move the star one square to the left

If after tossing the coin the star would move off the grid you stop.

What is the probability that you end up in the top left-hand corner of the grid for 2 x 2, 3 x 3, 4 x 4 and n x n grids?