# 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. - Mathematics and Statistics

Sum

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.

#### Solution

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

Concept: Concept of Probability
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