A pair of dice is thrown. Find the probability of getting 7 as the sum of it is known that hte second die always exhibits a prime number.

Explanation

A= represent second die show prime number

B= represents sum of the numbers on two dice is `7 `.

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

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


Then,

`
A cap B=(2,5),(5,2),(4,3)`

`
therefore P(B / A)=frac{n(A cap B)}{n(A)}=frac{3}{18}=frac{1}{6}`