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A darts player practises throwing a dart at the bull’s-eye on a dart board. Independently for each throw, her probability of hitting the bull’s-eye is 0.2. Let X be the number of throws she makes, up to and including her first success.

(a) Find the probability that she is successful for the first time on her third throw.

(b) Write down an equation for the probability distribution of X

(c) Find the probability that she will have at least 3 failures before her first success.

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