A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.

Question

Philoid · Accepted Answer

According to question, A and B throw a pair of dice alternately.

A wins if he gets a total of 6

∴ A = {(2,4), (1,5), (5,1), (4,2), (3,3)}

And B wins if she gets a total of 7

∴B = {(2,5), (1,6), (6,1), (5,2), (3,4), (4,3)}

Let P(B) is the probability, if A wins in a throw

And P(B) is the probability, if B wins in a throw

∴probability of winning the game by A in third throw