A fair die is tossed repeatedly. `A` wins if if is 1 or 2 on two consecutive tosses and `B` wins if it is 3,4,5 or 6 on two consecutive tosses. The probability that `A` wins if the die is tossed indefinitely is `1//3` b. `5//21` c. `1//4` d. `2//5`

Options

A. `1//3`
B. `5//21`
C. `1//4`
D. `2//5`

Answer

B

Explanation

Let `P(S)=P(1 or 2)=1//3`
`P(F)=P(3or4or5or6)=2//3`
`P(A "wins")=P[(SS orSFSSorSFSFSSor..)or(FSSorFSFFSSor...)]`
`=((1)/(9))/(1-(2)/(9))+((2)/(27))/(1-(2)/(9))`
`= 1/9xx9/7+2/27xx9/7`
`=1/7+2/21=(3+2)/(21)=5/21`
P(A swining)`=5/21,` P(B winning)`=16/21`