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.

Given: two dice are thrown at the same time and the product of numbers appearing on them is noted

To find: the probability that the product is a prime number

Explanation: Total number of outcomes of one dice = 6

So total number of outcomes = 6 × 6 = 36

So, n(S) = 36

And all the outcomes of S are

S = {(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)}

Let E denote outcomes such that the product is prime (i.e., having only factors), then the favourable outcomes of event E are

E = {(1,2), (1,3), (1,5), (2,1), (3,1), (5,1)}

Hence number of outcomes of E are n(E) = 6

Hence the probability that the product is a prime number is

P (getting the product is a prime number)

Substituting corresponding values, we get

Hence the probability that the product is a prime number is .