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. Select the correct answer from above options

Answer 1

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