A pair of unbiased dice are rolled together till a sum of “either 5 or 7” is obtained. Then find the probability that 5 comes before 7.

Options

A. `2//5
B. `3//5`
C. `4//5`
D. None of these

Explanation

Let A denote the event that a sum of 5 occurs, B the event that a sum of 7 occurs, and C the event that neither a sum of 5 nor a sum of 7 occurs. We have.
`P(A)=4/36=1/9,P(B)=6/36=1/6`
`P(C)=26/36=13/18`
Thus, probability that A occurs before B is
`P[A or (CnnA)or(CnnCnnA)or....]`
`=P(A)+P(CnnA)+P(CnnCnnA)+...`
`=P(A)+P(C)P(A)+P(C)^(2)P(A)+...`
`=1/9+((13)/(18))xx1/9+((13)/(18))^(2)1/9+...`
`=(1//9)/(1-13//18)=2/5`