18. Let f_n denote the number of ways of tossing a coin n times such that successive heads never appear. Argue that f_n = f_n-1 + f_n-2

n ≥ 2, where f₀ = 1, f₁ = 2 HINT: How many outcomes are there that start with a head, and how many start with a tail?

If P_n denotes the probability that successive heads never appear when a coin is tossed n times, find P_n (in terms of f_n) when all possible outcomes of the n tosses are assumed equally likely. Compute P₁₀.