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Chapter 3: Q100SE (page 203)
From a production batch with 16 items, 8 items are randomly selected for quality assurance. In how many different ways can the sample be drawn? Suggest an estimate before computing the exact number.
There are 12870 different ways in which the samples can be drawn.
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Forensic evidence in a criminal court case. In our legal system,the use of DNA as forensic evidence is often regarded as the most reliable type of evidence. However, most of the DNA code is the same for all humans. Consequently, assessing the probability of the DNA code that varies among individuals is the key to a successful case. Chance (Vol. 28, 2015) published an article on the use of DNA in a criminal case. The evidence found at the crime scene consisted of two alleles (sequences of DNA code), denoted {6/9}. One of these alleles comes from the individual鈥檚 mother and one from the individual鈥檚 father, but it is not known which allele-6 or 9-is from which parent. In forensic science, it is assumed that the two outcomes (alleles) are independent.
Are you really being served red snapper? Red snapper is arare and expensive reef fish served at upscale restaurants. Federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. Researchers
at the University of North Carolina used DNA analysis to examine fish specimens labeled 鈥渞ed snapper鈥� that were purchased from vendors across the country (Nature, July 15, 2004). The DNA tests revealed that 77% of the specimens were not red snapper but the cheaper, look-alike variety of fish.
a. Assuming the results of the DNA analysis are valid, what is the probability that you are actually served red snapper the next time you order it at a restaurant?
b. If there are five customers at a chain restaurant, all who have ordered red snapper, what is the probability that at least one customer is actually served red snapper?
Fuzzy logic in supply chain management. A branch of mathematics known as fuzzy logic was used to improve customer service in supply chain management. (Decision Analytics, February 2014.) Customers rate the importance of one service factor relative to another using the following numerical scale: 1 = service factors are equally important, 3 = one factor is moderately more important, 5 = one factor is strongly more important, 7 = one factor is very strongly more important and 9 = one factor is extremely more important. Fuzzy numbers were developed to allow for variation in customer responses. For example, the fuzzy number 1鈭紃epresents an actual response of either 1 or 3; the fuzzy number 7鈭紃epresents a response of 5, 7, or 9. Consider the probabilities of the actual responses for each fuzzy number shown in the table.
Fuzzy Response | Probabilities of Actual Responses |
a. If a customer gives a fuzzy response, what is the probability that the actual response is not a 7?
b. If both represent a possible fuzzy response of a customer, what are the possible actual responses for this customer?
Study of why EMS workers leave the job.Refer to the Journal of Allied Health(Fall 2011) study of why emergencymedical service (EMS) workers leave the profession,Exercise 3.45 (p. 182). Recall that in a sample of 244former EMS workers, 127 were fully compensated whileon the job, 45 were partially compensated, and 72 hadnon-compensated volunteer positions. Also, the numbersof EMS workers who left because of retirement were 7 forfully compensated workers, 11 for partially compensatedworkers, and 10 for no compensated volunteers.
a.Given that the former EMS worker was fully compensatedwhile on the job, estimate the probability that theworker left the EMS profession due to retirement.
b.Given that the former EMS worker had a non-compensatedvolunteer position, estimate the probabilitythat the worker left the EMS profession due toretirement.
c.Are the events {a former EMS worker was fully compensatedon the job} and {a former EMS worker left thejob due to retirement} independent? Explain.
Is a product 鈥済reen鈥�?A 鈥済reen鈥� product (e.g., a productbuilt from recycled materials) is one that has minimal impact on the environment and human health. How do consumers determine if a product is 鈥済reen鈥�? The 2011
ImagePower Green Brands Survey asked this question of more than 9,000 international consumers. The results are shown in the following table.
Reason for saying a product is green | Percentage of consumers |
Certification mark on label | 45 |
Packaging | 15 |
Reading information about the product | 12 |
Advertisement | 6 |
Brand we site | 4 |
Other | 18 |
Total | 100 |
a.What method is an international consumer most likely to use to identify a green product?
b.Find the probability that an international consumer identifies a green product by a certification mark on the product label or by the product packaging.
c.Find the probability that an international consumer identifies a green product by reading about the product or from information at the brand鈥檚 Web site.
d.Find the probability that an international consumer does not use advertisements to identify a green product.
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