On-the-job arrogance and task performance. Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 10% of all full-time workers will receive a poor performance rating. Also, assume that 5% of all full-time workers exhibit arrogant behaviors and receive a poor performance rating. Let A be the event that a full-time worker exhibits arrogant behavior on the job. Let B be the event that a fulltime worker will receive a poor performance rating.

a. Are the events A and B mutually exclusive? Explain.

b. Find P(B|A).

c. Are the events A and B independent? Explain.

Step 1 of 4:

We have the events A and B.

A = all full-time workers exhibit arrogant behaviors on the job.

B = all full-time workers will receive a poor performance rating.

AB = all full-time workers exhibit arrogant behavior and receive a poor performance rating.

P(A) = 0.15 (15%)

P(B) = 0.10 (10%)

P(AB) = 0.05 (5%)

Step 2 of 4:

the claim is to check the events A and B are mutually exclusiveIf the events are mutually exclusive, then P(AB) = 0.

Here, P(AB) = 0.05.

Hence, the events are not mutually exclusive.