Answer :

Number of oranges the box contains = 15

Number of good oranges = 12

Number of bad oranges = 3

Probability that box is approved for sale

= Probability that first orange is good × probability that second orange is good, given first is good × probability that third orange is good, given first two are good

Let A represents a good orange

Then P(A)=P(getting first orange as good)

And

P(A│A)=P(getting second orange good, given first is good)

(as now there are 11 good oranges left out of 14 total oranges as one good orange is already drawn in first draw and are not replaced)

And also,

P(AA│A)=P(getting third orange good, given first two are good)

(as now there are 10 good oranges left out of 13 total oranges as two good orange is already drawn in first draw and are not replaced)

So the probability that box is approved for sale is

Therefore probability that box is approved for sale is

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