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 one will be approved for sale.

Answer 1

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

Therefore, probability that first drawn orange is good, P(A)=$\frac{12}{15}$

Therefore, probability of getting second orange is good, P(A)= $\frac{11}{14}$

($\because$ The oranges are not replaced so number of good oranges left is 11)

Similarly, probability of getting third orange is good, P(C) = $\frac{10}{13}$

($\because$ The oranges are not replaced so number of good oranges left is 10)

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

Thus, probability of getting all the three oranges good = $\frac{12}{15}\times \frac{11}{14}\times \frac{10}{13}$

Therefore, the probability that the box is approved for sale = $\frac{44}{91}$.