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Chapter 3: Q36E (page 180)
Question: Refer to Exercise 3.35. Use the same event definitions to do the following exercises.
a. Write the event that the outcome is "On" and "High" as an intersection of two events.
b. Write the event that the outcome is "Low" or "Medium" as the complement of an event.
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A pair of fair dice is tossed. Define the following events:
A: [Exactly one of the dice shows a 1.]
B: [The sum of the numbers on the two dice is even.]
a. Identify the sample points in the events
b. Find the probabilities of all the events from part a by summing the probabilities of the appropriate sample points.
C. Using your result from part b, explain why A and B are not mutually exclusive.
d. Find using the additive rule. Is your answer the same as in part b?
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?
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?
Male nannies. In a survey conducted by the International Nanny Association (INA) and reported on the INA Web site (www.nanny.org), 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed were men. Find the probability that a randomly selected nanny placed during the last year is a male nanny (a 鈥渕annie鈥�).
Most likely coin-tossing sequence. In Parade Magazine鈥檚 (November 26, 2000) column 鈥淎sk Marilyn,鈥� the following question was posed: 鈥淚 have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three sequences was the result. One (and only one) of the sequences is genuine.鈥�
(1) H HHHHHHHHH
(2) H H T T H T T H HH
(3) T TTTTTTTTT
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