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This is an interesting and complicated scenario which will require clear probabilistic thinking. There will be various different ways in which the first part of the problem can be attempted, and it would be informative to compare and contrast these. It is quite a difficult problem and could be set to keen students individually or discussed collectively. It would be good as revision of a module on probability or to motivate the advanced study of probability.
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.
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?
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?