Question

A fair die is thrown two times. Find the probability that sum of the numbers on them is 5

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 A: Sum of the numbers on uppermost face is 5.

∴ A = {(1, 4), (2, 3), (3, 2), (4 ,1)}

∴ n(A) = 4

∴ P(A) = `("n"("A"))/("n"("S"))`

= `4/36`

= `1/9`.