MathDB

Will has a magic coin that can remember previous flips. If the coin has already turned up heads

m

times and tails

n

times, the probability that the next flip turns up heads is exactly

\frac{m+1}{m+n+2}

. Suppose that the coin starts at

0

flips. The probability that after

10

coin flips, heads and tails have both turned up exactly

5

times can be expressed as

\frac{m}{n}

for relatively prime positive integers

m

and

n

. Compute

m+n

.
Proposed by Nathan Xiong

Problem Statement