A fair die is rolled. The probability that the first time 1 occurs at the even throw, is :

Options

A. `(1)/(6)`
B. `(5)/(11)`
C. `(6)/(11)`
D. `(5)/(36)`

Answer

B

Explanation

Let `A_(i)` denote the event of getting 1, first time, in `i^(th)` throw.
Clearly,
p=Probability of getting 1 in a throw `=(1)/(6)`
q=Probability of not getting 1 in a throw `=(5)/(6)`
Required probability `=P(A_(2) cup A_(4) cup A_(6) cup..)`
`=P(A_(2))+P(A_(4))+P(A_(6))+P(A_(8))+..`
`=qp+q^(3)p+q^(5)p+q^(7)p+..`
`(qp)/(1-q^(2))=(5//36)/(1-(25)/(36))=(5)/(11)`