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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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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?

FA Cup

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

You'll need to work out, for each round, the probability that Arsenal play Chelsea and also the probability that they do not play against each other but both survive to play in the following round. A tree diagram is useful in thinking through this problem.