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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

Why do this problem?

A real world problem involving conditional probability.

Possible approach

Half the class might work through the problem with a probability of 0.4 of winning rallies against Ivana to see whether calling 9 or 10 isadvantageous, and the other half might work on the problem with a probability of 0.3. Then a class discussion, and drawing tree diagrams of the possibilites, might help everyone to solve the problem for a general value of p and find the critical value.

Key question

What are the possible outcomes of the next rally, which is served by Ivana, if my probability of winning the rally is p?

What happens if Ivana loses that rally?

See Also

There is a detailed explanation of the solution to this problem in this article.