You may also like

problem icon

Rain or Shine

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

problem icon

Squash

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

problem icon

Snooker

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Ante Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Draw a tree diagram to get started.
 
You could also fill in a table for all possible outputs for, say, the first 5 letters produced to get a feel for the problem and which sequences will win first. 
 
You can also read http://plus.maths.org/issue55/features/nishiyama/ which has answers to the required computations.