MathDB

Andy is planning to flip a fair coin 10 times. Among the 10 flips, Valencia randomly chooses one flip to exchange Andy's fair coin with her special coin which lands on heads with a probability of

\frac{1}{4}

. If the coin is exchanged in a certain flip, then that flip, along with all following flips will be performed with the special coin. The expected number of heads Andy flips can be expressed as

\frac{m}{n}

where

m

and

n

are positive integers. Find

m+n

.
Proposed by Andy Xu

Problem Statement