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 full-time 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.