Question

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is ______.

Options

• `1/18`

• `5/18`

• `1/5`

• `2/5`

Answer 1

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is `1/5`.

Explanation:

Let E₁ be the event showing the sum of the numbers on the two dice was less than 6 and E₂ be the event that the sum of the numbers is 3.

∴ E₁ = {(1, 1), (1, 2), (2, 1), (1, 3), (3, 1), (1, 4), (4, 1), (2, 2), (2, 3), (3, 2)}

n(E₁) = 10

And E₂ = {(1, 2), (2, 1)}

⇒ n(E₂) = 2 and n(E₁ ∩ E₂) = 2

∴ Required probability `"P"("E"_2/"E"_1) = ("n"("E"_1 ∩ "E"_2))/("n"("E"_1))`

= `2/10`

= `1/5`