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Question
Refer to Question 74 above. The probability that exactly two of the three balls were red, the first ball being red, is ______.
Options
`1/3`
`4/7`
`15/28`
`5/28`
Solution
Refer to Question 74 above. The probability that exactly two of the three balls were red, the first ball being red, is `4/7`.
Explanation:
Let E1 be the event that first ball is red.
E2 be the event that exactly two of the three balls are red.
∴ P(E1) = P(R) . P(R) . P(B) + P(R) . P(R) . P(R) + P(R) . P(B) . P(R) + P(R) . P(B) . P(B)
= `5/8*4/7*3/6 + 5/8*4/7*3/6 + 5/8*3/7*4/6 + 5/8*3/7*2/6`
= `60/336 + 60/336 + 60/336 + 30/336`
= `210/336`
P(E1 ∩ E2) = P(R) . P(B) . P(R) + P(R) . P(R) . P(B)
= `5/8*3/7*4/6 + 5/8*4/7*3/6`
= `60/336 + 60/336`
= `120/336`
∴ `"P"("E"_2/"E"_1) = ("P"("E"_1 ∩ "E"_2))/("P"("E"_1))`
= `(120/336)/(210/336)`
= `4/7`
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