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.

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

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

Probability

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