In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that :

(i) it is acceptable to a trader who accepts only a good shirt ?

(ii) it is acceptable to a trader who rejects only a shirt with major defects ?

We have,

Total number of shirts = 50

∴ No. of possible outcomes = 50.

(i) As, trader accepts only good shirts and number of good shirts = 44.

∴ No. of favourable outcomes = 44

P(trader will accept) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{44}{50} = \dfrac{22}{25}$.

Hence, the probability that a shirt is acceptable to a trader who accepts only a good shirt = $\dfrac{22}{25}$.

(ii) As, trader rejects shirts with major defects only and number of shirts with major defects = 2.

No. of shirts that trader will accept = 50 - 2 = 48.

∴ No. of favourable outcomes = 48

P(trader will accept) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{48}{50} = \dfrac{24}{25}$.

Hence, the probability that a shirt is acceptable to a trader who rejects only a shirt with major defects = $\dfrac{24}{25}$.