Three dice are thrown at the same time.
Question:

 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 six.

Solution:

Given that the dice is thrown three times

So, the sample space n(S) = 63 = 216

Let E1 be the event when the sum of number on the dice was 6 and E2 be the event when three 2’s occur.

E1 = {(1, 1, 4), (1, 2, 3), (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 [Since, E2 = (2, 2, 2)]

Thus, P(E2/E1) = P(E⋂ E2)/P(E1) = (1/216)/(10/216) = 1/10.

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