Question

A pair of dice is thrown once. The probability that the sum of numbers appearing on top faces is at least 4 is ______.

Options

• `1/11`

• `10/11`

• `5/6`

• `11/12`

Answer 1

A pair of dice is thrown once. The probability that the sum of numbers appearing on top faces is at least 4 is `bbunderline(11/12)`.

Explanation:

A pair of dice is thrown once.

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)}

Total possible outcomes = 36

Sum less than 4 occurs for = {(1, 1), (1, 2), (2, 1)} = 3

So, outcomes with a sum of at least 4 = 36 − 3 = 33

Required probability = `33/36`

= `11/12`