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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?

Succession in Randomia

Stage: 5 Challenge Level: Challenge Level:1

You can try an experiment to test this method but you will need to repeat the trials many times to reach any convincing conclusion. This would be a good class project.

A tree diagram will help you to analyse what happens. Try calculating the probabilities for 2, 3, 4, 5 and 6 ... tosses and see if you can identify a pattern emerging.

You could try to calculate the final probabilities. Theoretically the coin tossing can go on for ever so you will need to know a bit about summing an infinite series.