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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. |
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Answer» 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+...)` `P(B)= 1/9((8/9)/(1-(8/9)^2)) =(81**8)/(17**81) = 8/17` |
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