2014 AMC 12B Problems/Problem 22
A long, but straightforward bash:
Define P(N) to be the probability that the frog survives starting from pad N.
Then note that by symmetry, P(5) = 1/2, since the probabilities of the frog moving subsequently in either direction from pad 5 are equal.
We therefore seek to rewrite P(1) in terms of P(5), using the fact that
P(N) =
as said in the problem.
Hence P(1) =
Returning to our original equation:
Returning to our original equation:
Cleaing up the coefficients, we have:
Hence, P(1) =
=