A and B having equal skill, are playing a game of three points. After A has won 2 points and B has won 1 point, what is the probability that A will win the game?
I tried to solve the above problem using a counting diagram given below.
Given that A has already two of the first three points, the diagram below shows all cases for A to be a winner. A can win in 6 different ways if A has 2 of 3 points already. We don't need to play the 5th point if A has already won in 4th point, which is considered in the diagram.
Also, total number of cases is 9. So, probability that A will win given the pre- condition is 6/9 = 2/3.
I am not sure if my counting diagram is incomplete. It seems ok to me.
The answer given in the book is 3/4.
