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Question
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale
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Solution
Let the events of getting a good orange in the first, second and third draw be A, B and C respectively.
Then required probability = P(A ∩ B ∩ C)
Now P(A) = probability of getting a good orange in the first draw = `12/15 xx 4/5`
After taking out one good orange in the first draw, the number of remaining oranges is 14 out of which 11 oranges are good.
∴ P(B|A) = `11/14`
In the second draw also, after taking out one good orange, there are 13 oranges remaining, of which 10 oranges are good.
∴ P(C|A ∩ B) = `10/13`
∴ Required probability = P(A ∩ B ∩ C) = P(A). P(B|A). P(C|A ∩ B)
= `4/5 xx 11/14 xx 10/13`
= `44/91`
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