Question

Three dice are thrown at the sametime. Find the probability of getting three two’s, if it is known that the sum of the numbers on the dice was six.

Answer 1

The dice is thrown three times

∴ Sample space n(S) = (6)³ = 216

Let E₁ be the event when the sum of numbers on the dice was six and E₂ be the event when three two’s occur.

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

⇒ n(E₁) = 10 and n(E₂) = 1   ......[∵ E₂ = {2, 2, 2}]

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

= `(1/216)/(10/216)`

= `1/10`.