Two persons `A` and `B` take turns in throwing a pair of dice. The first person to throw `9` from both dice will be awarded the prize. If A throws first, then the probability that `B` wins the game is

Options

A. a) `9/17`
B. b) `8/17`
C. c) `8/9`
D. d) `1/9`

Answer

b) `8/17`

Explanation

Total Sample space `=36`


Probability of getting `9` on two dice `= 4/36 = 1/9`


`P(A)=1/9`


`P(A') =1-1/9= 8/9`


`A` will win if throwing 9 in odd number of attempts.


`B` will win if throwing `9` in even number of attempts.


Required probability `= (8/9)*(1/9) + (8/9)^3*(1/9) + … `


`= ((8/9)(1/9)) / [1- (8/9)^2]`


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