A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three orange 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.

44/91

Let A, B and C be the respective events that the first, second, and the third drawn orange is good.

Therefore, probability that first drawn orange is good, P(A) = 12/15

The oranges are not replaced.

Therefore, the probability of getting second orange good, P(B) = 11/14

Similarly, probability of getting third orange good, P(C) = 10/13

The box is approved for sale, if all the oranges are good.

Thus the probability of getting all the oranges good = (12/15) x (11/14) x (10/13) = 44/91

Therefore, the probability that the box is approved for sale is 44/91