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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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If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

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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?

Ante Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Draw a tree diagram to get started.
You could also fill in a table for all possible outputs for, say, the first 5 letters produced to get a feel for the problem and which sequences will win first. 
You can also read which has answers to the required computations.