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.)

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windyyork windyyork · Answer 1 · 2019-07-23T09:25:51+02:00

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

Step-by-step 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 [tex]p(unqualified\mid approved)=\dfrac{0.06}{0.7225+0.06}=\dfrac{0.06}{0.7825}=0.0766[/tex]

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