Question

A coin has probability p of showing head when tossed. It is tossed n times. Let p_n denotes the probability that no two (or more)-consecutive heads occur. Prove that p₁ = 1. p₂ = 1 and p_n = (1 - p). p_{n - 1} + p(1 - p)p_{n - r} or all n ≥ 3.

Answer 1

Since, p_n  denotes the probability that no two (or more) consecutive heads occur. 

→ p_n denotes the probability that I or no head occur. 

For n = 1, p₁ = 1 because in both cases we get less than two heads (H, T).