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Nov 2021 p53 q6
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In a game, Jim throws three darts at a board. This is called a ‘turn’. The centre of the board is called the bull’s-eye.
The random variable \(X\) is the number of darts in a turn that hit the bull’s-eye. The probability distribution of \(X\) is given in the following table.
| \(x\) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \(P(X = x)\) | 0.6 | p | q | 0.05 |
It is given that \(E(X) = 0.55\).
- (a) Find the values of \(p\) and \(q\).
- Jim is practising for a competition and he repeatedly throws three darts at the board.
- (c) Find the probability that \(X = 1\) in at least 3 of 12 randomly chosen turns.
- (d) Find the probability that Jim first succeeds in hitting the bull’s-eye with all three darts on his 9th turn.
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