# A fair die is thrown two times. Find the chance that Sum of the numbers on the upper face is at least 10. - Mathematics and Statistics

Sum

A fair die is thrown two times. Find the chance that Sum of the numbers on the upper face is at least 10.

#### 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 C: Sum of the numbers on the upper most face is at least 10 (i.e. 10, 11 or 12)
C = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
∴ n(C) = 6

∴ P(C) = ("n"("C"))/("n"("S")

= 6/36

= 1/6

Concept: Elementary Properties of Probability
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