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Thank Your Lucky Stars

Age 14 to 16
Challenge Level Yellow starYellow star
  • Problem
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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?

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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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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