Three dice are thrown at the same time. Find the probability of getting three two's, if it is known that the sum of the numbers on the dice was 6

Explanation

As three dice are thrown, sample space `n(s) = 6^3 = 216`

Let `A` is the event when sum of the numbers on three dice is `6` and

`B` is the event when three twos occurs.

Then, `A = {(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(A) = 10`

`:.P(A) = 10/216`

`B = {(2,2,2)}`

`n(B) = 1`

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