Question

A fair die is thrown two times. Find the probability that the product of numbers on them is 12.

Answer 1

When a fair die is tossed twice, the sample sp ace S is given by

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)}

∴ n (S) = 36

Let D = the event that product of numbers is 12

∴ D = {(2, 6), (3, 4), (4, 3), (6, 2)}

∴ n(D) = 4

∴ P(D) = `("n"("D"))/("n"("S"))`

= `4/36`

= `1/9`