Question

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.

Answer 1

Total no.of possible outcomes = 6^2 = 36

i.e. (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)

Out of these,product of outcomes that would be prime would be (1,2),(1,3),(1,5),(2,1),(3,1),(5,1).

Probability = 6/36 = 1/6