Question

Given that two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4.

Options

• `2/36`

• `30/36`

• `1/15`

• `1/6`

Answer 1

`1/15`

Explanation:

When the numbers appearing on throwing two dice, are different.

⇒ The numbers are not the same.

Total number of exhaustive cases = 36

No. of cases when doubits do not occus = 36 – 6 = 30 cases when he sum is 4 are {(1, 3), (2, 2), (3,1)}

Let 'A' denotes the event when the sum of numbers on two dice is 4.

'B' is the event when the numbers appearing on the dice are different.

A ∩ B = |(1, 3), (3, 1)|

P(A ∩ B) = `2/36`, P(B) = P(B) = `30/36`

P(A/B) = `(P(A ∩ B))/(P(B)) = 2/36 + 30/36 = 1/15`