Question

Two dice are thrown. Find the probability of the following events:

1. Event A: The sum of the numbers on their upper faces is at least 9.

2. Event B: The sum of the numbers on their upper faces is divisible by 5.

3. Event C: The number on the upper face of the first die is greater than the number on the upper face of the second die.

Answer 1

The sample space

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

a. Event A: The sum of the numbers on their upper faces is at least 9.

∴ A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

∴ n(A) = 10

`P(A) = (n(A))/(n(S))`

∴ P(A) = `10/36`

∴ P(A) = `5/18`

b. Event B: The sum of the numbers on their upper faces is divisible by 5.

∴ B = {(1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)}

∴ n(B) = 7

∴ `P(B) = (n(B))/(n(S))`

∴ P(B) = `7/36`

c. Event C: The number on the upper face of the first die is greater than the number on the upper face of the second die.

∴ C = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3), (5, 4), (6, 1) (6, 2), (6, 3), (6, 4), (6, 5)}

∴ n(C) = 15

`P(C) = (n(C))/(n(S))`

∴ P(C) = `15/36`

∴ P(C) = `5/12`