Question

A fair die is thrown two times. Find the probability that the first throw gives a multiple of 2 and the second throw gives a multiple of 3.

Answer 1

When two dice are thrown, the sample space is

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 event C: First throw gives a multiple of 2 and second throw gives a multiple of 3.

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

∴ n(C) = 6

∴ P(C) = `("n"("C"))/("n"("S"))`

 = `6/36`

= `1/6`