A and b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by
a.

(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)

A and b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by a.

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A and b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by
a.