Chapter 4: Q1 (page 166)
Language: Complement of “At Least One” Let A = the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing event.
is the event of getting no defective iPhone out of the three selected iPhones.
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Acceptance Sampling. With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is found to be okay. Exercises 27 and 28 involve acceptance sampling.
Defective Pacemakers Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from “Pacemaker and ICD Generator Malfunctions,” by Maisel et al., Journal of the American Medical Association, Vol. 295, No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters or a \(1 bill, college students were given either four quarters or a \)1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).
Purchased Gum | Kept the Money | |
Students Given Four Quarters | 27 | 46 |
Students Given a $1 bill | 12 | 34 |
Denomination Effect
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.
c. What do the preceding results suggest?
Sobriety Checkpoint When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that = 0.00888, where I denotes the event of screening a driver and getting someone who is intoxicated. What does denote, and what is its value?
In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.
Square Peg Sydney Smith wrote in “On the Conduct of the Understanding” that it is impossible to fit a square peg in a round hole.
In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.
McDonald’s | Burger King | Wendy’s | Taco Bell | |
Order Accurate | 329 | 264 | 249 | 145 |
OrderNotAccurate | 33 | 54 | 31 | 13 |
Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order that is not accurate or is from Wendy’s. Are the events of selecting an order that is not accurate and selecting an order from Wendy’s disjoint events?
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