# Exam Style Question

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Question id: 49. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is not allowed.

### Probability

Jane and David play two games of golf. The probability that Jane wins the first game is $$\frac56$$. If Jane wins the first game, the probability that she wins the second game is $$\frac67$$.

If Jane loses the first game, the probability that she wins the second game is $$\frac34$$

(a) Copy and complete the following tree diagram.

(b) Find the probability that Jane wins the first game and David wins the second game.

(c) Find the probability that David wins at least one game.

(d) Given that David wins at least one game, find the probability that he wins both games.

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