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Rain or Shine

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

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Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

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A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?


Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

See the similar problem Snooker for ideas on how to do this calculation.