Problem:
A coin that comes up heads with probability and tails with probability independently on each flip is flipped eight times. Suppose the probability of three heads and five tails is equal to of the probability of five heads and three tails. Let , where and are relatively prime positive integers. Find .
Solution:
The conditions of the problem imply that , and hence , so that . Thus , and .
The problems on this page are the property of the MAA's American Mathematics Competitions