MathDB
Another Biased Coin...

Source:

February 19, 2006
probabilityAMCAIME

Problem Statement

When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to 00 and is the same as that of getting heads exactly twice. Let ij\frac ij, in lowest terms, be the probability that the coin comes up heads in exactly 33 out of 55 flips. Find i+ji+j.