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 three are bad ones, will be approved for sale.

Answer 1

Box contains 12 good and 3 bad oranges. If three oranges selected are good ones, the box is approved for sale.

3 good oranges may be selected in12C3 ways.

3 oranges out of 15 may be selected in15C3 ways.

Probability that a box is approved

= Probability of selecting 3 good oranges

= \(\frac{{ }^{12} C_{3}}{{ }^{15} C_{3}}\) = \(\frac{12×11×10}{15×14×13}\) = \(\frac{44}{91}\).