Three player `A, B and C`, toss a coin cyclically in that order (that is `A, B, C, A, B, C, A, B,...`) till a headshows. Let p be the probability that the coin shows a head. Let `alpha, beta and gamma` be, respectively, the probabilities that `A, B and C` gets the first head. Then determine `alpha, beta and gamma` (in terms of p).

Options

A. `alpha = p/(1-q^(3))`, where q = 1 - p
B. `beta = (p(1-p))/(1-q^(3))`
C. `gamma = (p-2p^(2)+P^(3))/(1-q^(3))`
D. All of these

Answer

D