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.

Explanation

Let A denote the event that a wim of 5 occurs, B the event that a sum of 7 occurs and C be 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=1/6and P(C)=26/36=13/18`
Thus, P(A occurs before B) `=1/9+((13)/(18))xx1/9+((13)/(18))^(2)1/9+...=(1//9)/(1-13//18)=2/5`