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

We know, when a pair of dice is thrown, total possible outcomes are = 36

A=No of outcomes for getting 7 as sum are {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} = 6

Therefore, P(A) = 6/36 =

B= No of outcomes for second die exhibiting prime no =

{(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)} = 18 {since 2,3,5 are prime nos )

Hence P(B) =

(A B) = outcomes of getting 7 as a sum with a second die showing prime no

= {(2,5), (5,2),(4,3)} = 3

Hence P(A B) = 3/36 =

Therefore, = = (answer)