Alvin, Simon and Theodore are playing a simple dice game in which they take

turns rolling a fair die. A player wins when he rolls a die and one of his favorite numbers shows

on the die. Alvin's numbers are 1, 2 and 3, Simon's numbers are 4 and 5, and Theodore's

number is 6. Suppose that Theodore goes rst, Simon goes second, and Alvin goes last. Also

note that if no player gets one of his numbers on the rst round, then they keep rolling the die

until there is a winner.

What is the probability that Alvin wins this game?