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.
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.

Solution:

Given: A box of oranges.

Let A, B, and C represent the events that occur when the first, second, and third drawn oranges are all excellent.

Now, (good orange in first draw) .
Because the second orange is not replaced, the total number of excellent oranges will now be 11 and the total number of oranges will be 14, which is the conditional probability of B if A has already occurred.

Now, good orange in second draw

Because the third orange is not replaced, the total number of excellent oranges is now 10 and the total number of orangs is 13, which is the conditional probability of C provided that and have already occurred.

Now, (good orange in third draw)

As a result, there’s a strong chance that all of the oranges are excellent.

As a result, the likelihood of a box being authorised for sale is high.