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

Options

A. `(1)/(6)`
B. `(1)/(3)`
C. `(2)/(7)`
D. `(3)/(5)`

Answer

B

Explanation

Let `A =((1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}`
and `B={(1,2),(2,1),(2,2),(3,2),(2,3),(4,2),(2,4),(5,2),(2,5),(6,2),(2,6)}`
`:. A nn B ={(2,5),(5,2)}`
`P(B//A) =(n(A nnB))/(n(A)) =(2)/(6)=(1)/(3)`