Chapter 2, Problem 2.18TE

Let $f_n$, denote the number of ways of tossing a coin n times such that successive heads never appear. Argue that $f_n=f_{n-1}+f_{n-2}n\ge 2$, where $f_0\equiv 1f_2\equiv 2$

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 $P_n$.