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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.
Solution
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`.
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