MathDB

Zou and Chou are practicing their 100-meter sprints by running

6

races against each other. Zou wins the first race, and after that, the probability that one of them wins a race is

\frac23

if they won the previous race but only

\frac13

if they lost the previous race. The probability that Zou will win exactly

5

of the

6

races is

\frac mn

, where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement