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Two person A and B take turns in throwin...

Two person `A and B` take turns in throwing a pair of dice. The first person to through 9 from both dice will win the game. If A throwns fisrt then the probability that B wins the game is.

Text Solution

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Total number of ways sum of both dice can come `9 = 4`
Total number of combinations of both dice `= 6**6 = 36`
`:.` Probability of winnining, `P(W) = 4/36 = 1/9`
Probability of losing, `P(L) = 1-1/9 = 8/9`
As A starts first probability of B winning in first attempt`= 1/9**8/9`
Probability of B winning in second attempt `= 8/9**8/9**8/9**1/9=(8/9)^3**1/9`
Probability of B winning in third attempt `= (8/9)^5**1/9`
`:.` Probability of B winning `P(B)= 1/9(8/9+(8/9)^3+(8/9)^5+...)`
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