A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
Total possible outcomes for A winning the game = 6
Sample space = 36 outcomes.
P( A winning) = 1/6
Hence, A' =5/6
Total possible outcomes for B winning the game = 3
P(B winning the game) = 1/12
Hence, 11/12
Since, A starts the game therefore, the probability that B wins the game is
(5/6 x 1/12) + (5/6 11/12 x 5/6 x 1/12) + ... and so on till infinite terms.
Hence, a= 5/72 and r = 55/72
Therefore, Probability that B wins the game = 5/72 / 1-55/72 = 5/17