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A fair die is thrown two times. Find the chance that product of the numbers on the upper face is 12. - Mathematics and Statistics

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Sum

A fair die is thrown two times. Find the chance that product of the numbers on the upper face is 12.

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Solution

If a fair die is thrown twice, 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 A: Product of the numbers on the uppermost face is 12.
A = {(2, 6), (3, 4), (4, 3), (6, 2)}
∴ n(A) = 4

∴ P(A) = `("n"("A"))/("n"("S"))`

= `4/36`

= `1/9`

Concept: Elementary Properties of Probability
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