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?
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?

Solution:

We have,

Total number of shirts = 50

Total number of elementary events = 50 = n(S)

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

Event of accepting good shirts = 44 = n(E)

Probability of accepting a good shirt = n(E)/ n(S) = 44/50 = 22/25

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

Event of accepting shirts = 50 – 2 = 48 = n(E)

Probability of accepting shirts = n(E)/ n(S) = 48/50 = 24/25