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.

Options

A. `(9)/(17)`
B. `(8)/(17)`
C. `(8)/(9)`
D. `(1)/(9)`

Answer

B

Explanation

The probability of throwing 9 with two dices
`=(4)/(36)=(1)/(9)`
`therefore` The probability of not throwing 9 with two dices `=1-(1)/(9)=(8)/(9)`
If A is to win, he should throw 9, in 1st or 3rd or 5th and so on
If B is to win, he should throw 9 in 2nd or 4th and so on
B can get the chance only when A should not get it.
P(B' s win)`=(8)/(9)*(1)/(9)+((8)/(9))^(3)*(1)/(9)+ ...`
`=((8)/(9)xx(1)/(9))/(1-((8)/(9))^(2))=(8)/(17)`