maihuna wrote:A and B throw a die alternatively till one of them gets a ‘6’ and wins the
game. Find their respective probabilities of winning, if A starts first.

1/11
5/11
6/11
1/6
5/6

If A gets a 6 he win with probability 1/6. If he loses he does so with probability 5/6. So the winning series will go like this


A B A B A
W LW LLW LLLW LLLLW LLLLLW


A wins sequence

1/6 (5/6)^2 x 1/6 (5/6)^4 1/6 .....

B wins sequence

5/6 1/6 (5/6)^3 1/6 (5/6)^5 1/6

A's geometric sequence has a=1/6 geometric ratio = (5/6)^2

The sum of the series is

1/6/1-(5/6)^2 =6/11


A wins with probability 6/11

B wins with probability 5/11