MathDB

Yor and Fiona are playing a match of tennis against each other. The first player to win

6

games wins the match (while the other player loses the match). Yor has currently won

2

games, while Fiona has currently won

0

games. Each game is won by one of the two players: Yor has a probability of

\frac23

to win each game, while Fiona has a probability of

\frac13

to win each game. Then,

\frac{m}{n}

is the probability Fiona wins the tennis match, for relatively prime integers

m,n

. Compute

m

Problem Statement