A die is rolled twice and the sum of the numbers appearing on them is observed to be 7.What is the conditional probability that the number 2 has appeared at least once?

A) 1/3    B) 2/3    C) 12/15    D) 2/9

Consider the following events:

A=Getting number 2 at least once,

B=Getting 7 as the sum of the number on two dice.

We have,A={(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(1,2),(3,2),(4,2),(5,2),(6,2)}

And={ (2,5),(5,2),(6,1),(1,6),(3,4),(4,3)}

∴P(A)=11/36,P(B)=6/36 and P(A∩B)=2/36

So, Required probability =P(A/B)=P(A∩B)/P(B)=2/36/6/36=1/3