A, B and C roll dice. They use fair dice. That is, the probability of any of the 6 sides coming up is 1/6. A starts by rolling a die, then B rolls a die, then C rolls a die, then A again, and so on. The winner of the game is the first one to get a 6''. Let A=''A wins'' denote the event that A wins, B= B wins'' and C=''C wins''.

1) Find the probability that A wins. That is, find . Give your answer correct to two decimal places.

Hint: use the law of total probability with E1= "A wins in round 1", E2= "B or C wins in round 1", E3= "nobody wins in round 1".

2) Find Pr(B)

3) Find Pr(A|B complement)