Example 36 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 Solution Let S denote the success (getting a ‘6’) and F denote the failure (not getting
a ‘6’) Thus,
P(S) = 1
5
6, P(F)
6
=
P(A wins in the first throw) = P(S) = 1
6
A gets the third throw, when the first throw by A and second throw by B result into
failures