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.

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.

Philoid · Accepted Answer

Given: A box of oranges.

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

Now, P(A) = P(good orange in first draw) =

Because the second orange is drawn without replacement so, now the total number of good oranges will be 11 and total oranges will be 14. i.e. the conditional probability of B given that A has already occurred.

Now, P = P(good orange in second draw) =

Because the third orange is drawn without replacement so, now the total number of good oranges will be 10 and total orangs will be 13. i.e. the conditional probability of C given that A nd B has already occurred.

Now, P= P(good orange in third draw) =

Thus the probability that all the oranges are good:

⇒ P(A ∩ B ∩ C) =

Hence, the probability that a box will be approved for sale