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A fair die is tossed repeatedly. A wins ...

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 a.`1//3` b. `5//21` c. `1//4` d. `2//5`

A

`(1)/(3)`

B

`(1)/(4)`

C

`(5)/(21)`

D

`(2)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Let event `S to A` is getting `1` or `2`
Event `F to B` is getting `3,4,5,6`
`P(S)=P(1 or 2)=1//3`
`P(F)=P(3 or 4 or 5 or 6)=2//3`
`P(A"wins")=P[(SS or SFSS or SFSFSS or ….) or (FSS or FSFSS or….)]`
`=((1)/(9))/(1-(2)/(9))+((2)/(27))/(1-(2)/(9))`
`=(1)/(9)xx(9)/(7)+(2)/(27)xx(9)/(7)`
`=(5)/(21)`
`P(A"winning")=(5)/(21)`
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