Three people, call them Alison, Barbara, and Cuthbert, engage in a novel dart game in which balloons are targets. Each contestant has one balloon and remains in the game as long as their balloon is unbroken. The winner is the player who is left with the sole surviving balloon.

Each round, the contestants who remain in the game draw lots to determine the order of play and then take turns throwing one dart apiece. They are all aware of their respective skill: Alison can pop a balloon 4 out of 5 times, Barbara can pop one 3 out of 5 times, and Cuthbert can pop one 2 out of 5 times. Assume that each player adopts the strategy of aiming at the balloon of their strongest opponent.

1. For each of the three, determine the probability that they will win in the first round.
2. What is the probability that Cuthbert will win in the second round?

from Archimedes revenge
by Paul Hoffman

Due Friday, February 26^th at Noon.