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9231 P23 - Jun 2019 - Q7 - 8 marks
6110

A pair of fair coins is thrown repeatedly until a pair of tails is obtained. The number of throws taken is denoted by the random variable \(X\).
(i) State the expected value of \(X\).

(ii) Find the probability that exactly 3 throws are required to obtain a pair of tails.

(iii) Find the probability that fewer than 4 throws are required to obtain a pair of tails.

(iv) Find the least integer \(N\) such that the probability of obtaining a pair of tails in fewer than \(N\) throws is more than 0.95 .

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