Question

Find the probability that a person is not qualified if he or she was approved by the manager. certain job, 85% are qualified and 15% are not. The personnel manager claims that she approves qualified people 85% of the time; she approves unqualified people 40% of the time. The probability is 0.15 (Type an integer or decimal rounded to four decimal places as needed.)

Answer 1

Answer: The probability that a person is not qualified if a person was approved by the manager is 0.0766.

Explanation:

Since we have given that

Probability that a person approves qualified = 0.85× 0.85 = 0.7225

Probability that a person does not approve qualified = 0.85 × 0.15 = 0.1275

Probability that a person approves unqualified = 0.40 × 0.15 = 0.06

Probability that a person does not approve unqualified = 0.60 × 0.15 = 0.009

so, using the conditional probability, we get that
`p(unqualified\mid approved)=(0.06)/(0.7225+0.06)=(0.06)/(0.7825)=0.0766`

Hence, the probability that a person is not qualified if a person was approved by the manager is 0.0766.