Chapter 3: Q97E (page 203)
Consider two events A and B, with,,and
a.Are A and B mutually exclusive?
b.Are A and B independent?
a. The events are mutually exclusive.
b. The events are not independent.
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Three fair coins are tossed and either heads(H) or tails(T) are observed for each coin.
A= {Three heads are observed}
B= {Exactly two heads are observed}
C= {At least two heads are observed}
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. 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.
Evaluating the performance of quality inspectors. The performance of quality inspectors affects both the quality of outgoing products and the cost of the products. A product that passes inspection is assumed to meet quality standards; a product that fails inspection may be reworked, scrapped, or reinspected. Quality engineers at an electric company evaluated performances of inspectors in judging the quality of solder joints by comparing each inspector’s classifications of a set of 153 joints with the consensus evaluation of a panel of experts. The results for a particular inspector are shown in the table. One of the 153 solder joints was selected at random.
Committee’s judgment joint | Joint Acceptable | joint Rejectable |
Joint Acceptable | 101 | 10 |
joint Rejectable | 23 | 19 |
a. What is the probability that the inspector judged the joint to be acceptable? That the committee judged the joint to be acceptable?
b. What is the probability that both the inspector and the committee judged the joint to be acceptable? That neither judged the joint to be acceptable?
c. What is the probability that the inspector and the committee disagreed? Agreed?
Workers’ unscheduled absence survey. Each year CCH, Inc., a firm that provides human resources and employment law information, conducts a survey on absenteeism in the workplace. The latest CCH Unscheduled Absence Surveyfound that of all unscheduled work absences, 34% are due to “personal illness,” 22% for “family issues,” 18% for “personal needs,” 13% for “entitlement mentality,” and 13% due to “stress.” Consider a randomly selected employee who has an unscheduled work absence.
a. List the sample points for this experiment.
b. Assign reasonable probabilities to the sample points.
c. What is the probability that the absence is due to something other than “personal illness”?
Drug testing in athletes.When Olympic athletes are tested for illegal drug use (i.e., doping), the results of a single positive test are used to ban the athlete from competition. Chance(Spring 2004) demonstrated the application of Bayes’s Rule for making inferences about testosterone abuse among Olympic athletes using the following example: In a population of 1,000 athletes, suppose 100 are illegally using testosterone. Of the users, suppose 50 would test positive for testosterone. Of the nonusers, suppose 9 would test positive.
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