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Question id: 7. This question is similar to one that appeared in an IB Standard paper in 2010. The use of a calculator is allowed.

### Probability

At the south end of Playfair Amusement park are two games of chance, Beat The Goalie and Basketball Bounce.

For the Goalie game, the probability of winning is 0.1. If someone plays this game nine times:

(a) Find the probability that they win exactly three times.

For the Basketball game, the probability of winning is $$x$$. If someone plays it nine times.

(b) Write down an expression, in terms of $$x$$, for the probability of winning exactly three games.

(c) Hence, find the values of $$x$$ such that the probability of winning exactly three games is 0.2.

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