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It may be helpful to consider an ordering of the events, with the associated probabilities at each stage.
For example, first the athletes decide whether to take the drug or not. Then the race takes place. Then the drug testing takes place.
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.
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?
A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?