There are 6*6 total combinations = 36 combinations.
For A: the probability that one rolls a 9 is 4/36
(9 = 3&6, 6&3, 4&5, 5&4)
For B: the probability that one rolls a 6 is 5/36
(6 = 3&3, 1&5, 5&1, 2&4, 4&2)
So find the probability that final roll is made by A:
P(A wins) = P(A
wins in first roll) + P(A wins in 3rd roll) + .....
P(A wins) = 4/36 + (32/36)*(31/36)*(4/36) +
(32/36)^2 *(31/36)^2 *(4/36) + ...
Therefore we see that the common ratio is (32*31/36^2)
Sum is = (4/36) / [1 - (32*31/36^2)]
= 144 / 304
= 9 / 19 (ANSWER)
