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Three players A, B and C toss a coin cyc...

Three players A, B and C toss a coin cyclically in that order (that is A, B, C, A, B, C, A, B,…) till a head shows. Let p be the probability that he coin shows a head. Let `alpha, beta and gamma` be respectively the probabilities that A, B and C gets the first head. Prove that `beta = (1 - p) alpha`. Determine, `alpha, beta and gamma` (in terms of p).

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The correct Answer is:
`alpha = (p)/(1-(1-p)^(3)),beta = (p(p-1))/(1-(1-p)^(3)),gamma = (p(p-1)(p-3))/(1-(1-p)^(3))`
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