Question
A and B throw a die alternately 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').
P(A wins in the first throw) = P(S)= 
A gets the throw, when the first throw by A and second throw by B result into failures. Therefore,
P(B wins) = 1 - P(A wins) = 
