Problem 61 Solution
Think of the problem as a random walk where the probability is p of moving to the left
and 1-p of moving to the right. The expected change in the position on the number
line per move is p*(+1) + (1-p)*(-1) = 2p-1. The first flip resulted in moving one
space to the right. The expected number of moves to move one space to the left is the
inverse of the expected movement, which equals 1/(2p-1).
It may not seem reasonable to take the last step on faith but millions of computer
trials have verified the answer.
Michael Shackleford, A.S.A.