Question

Of all the people applying for a certain​ job, 80% are qualified and 20​% are not. The personnel manager claims that she approves qualified people 90​% of the​ time; she approves unqualified people 10​% of the time. Find the probability that a person is not qualifiednot qualified if he or she was not approved by the manager.

Answer 1

Answer:

69.23% probability that a person is not qualified if he or she was not approved by the manager.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes:

In this problem, we have these following probabilities:

80% probability that a person is qualified

20% probability that a person is not qualified.

90% probability that a qualified person is approved.

10% probability that a qualified person is not approved.

10% probability that an unqualified person is approved.

90% probability that an unqualified person is not approved.

Find the probability that a person is not qualified if he or she was not approved by the manager.

Desired outcomes

Unqualified and not approved.

20% are not qualified. Of those, 90% were not approved. So

$0.9*0.2 = 0.18$

Total outcomes:

Qualified and not approved or unqualified and not approved.

80% are qualified. Of those, 10% were not approved

20% are not qualified. Of those, 90% were not approved. So

$0.8*0.1 + 0.9*0.2 = 0.26$

Probability

$P = \frac{0.18}{0.26} = 0.6923$

69.23% probability that a person is not qualified if he or she was not approved by the manager.