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Question
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is ______.
Options
`1/18`
`5/18`
`1/5`
`2/5`
Solution
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is `1/5`.
Explanation:
Let E1 be the event showing the sum of the numbers on the two dice was less than 6 and E2 be the event that the sum of the numbers is 3.
∴ E1 = {(1, 1), (1, 2), (2, 1), (1, 3), (3, 1), (1, 4), (4, 1), (2, 2), (2, 3), (3, 2)}
n(E1) = 10
And E2 = {(1, 2), (2, 1)}
⇒ n(E2) = 2 and n(E1 ∩ E2) = 2
∴ Required probability `"P"("E"_2/"E"_1) = ("n"("E"_1 ∩ "E"_2))/("n"("E"_1))`
= `2/10`
= `1/5`
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