Question

A machine produces photodetectors in pairs. Tests show that the first photo detector is acceptable with probability 3/5. When the first photo detector is acceptable, the second photo detector is acceptable with probability 4/5. If the first photo detector is defective, the second photo detector is acceptable with probability 2/5.

(a) Find the probability that exactly one photo detector of a pair is acceptable.

Answer 1

Answer: P(A or B) = 7/25

the probability that exactly one photo detector of a pair is acceptable is 7/25

Explanation:

Given:

The probability that the first photo detector is acceptable P(A)= 3/5

The Probability that the first photo detector is defective P(A') = 1 - P(A) = 1 - 3/5 = 2/5

The probability that the second photo detector is acceptable given that the first one is defective P(B|A')= 2/5

The probability that the second photo detector is defective given that the first one is acceptable P(B'|A) = 1 - 4/5 = 1/5

The probability that exactly one photo detector of a pair is acceptable is given as:

P(A/B) = P(A)P(B'|A) + P(A')P(B|A')

P(A/B) = 3/5 × 1/5 + 2/5 × 2/5

P(A/B) = 7/25