Question

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

Answer 1

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 B: Sum of the numbers on the uppermost face is 10.
B = {(4, 6), (5, 5), (6, 4)}
∴ n(B) = 3

∴ P(B) = `("n"("B"))/("n"("S"))`

= `3/36`

= `1/12`