Question

A carton consists of 100 shirts of which 88 are good and 8 have minor defects. Rohit, a trader, will only accept the shirts which are good. But Kamal, an another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to

(i) Rohit,
(ii) Kamal?

Answer 1

Total number of shirts = 100.
Number of good shirts = 88.
Number of shirts with minor defects = 8.
Number of shirts with major defects = 100 − 88 − 8 = 4.

(i) P(the drawn shirt is acceptable to Rohit) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{88}{100}=\frac{22}{25}$

Thus, the probability that the drawn shirt is acceptable to Rohit is $\frac{22}{25}$.

(ii) P(the drawn shirt is acceptable to Kamal) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{88+8}{100}=\frac{96}{100}=\frac{24}{25}$

Thus, the probability that the drawn shirt is acceptable to Kamal is $\frac{24}{25}$.