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Language: Complement of 鈥淎t Least One鈥� 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$\stackrel{炉}{A}$.

Critical Thinking: Interpreting results from a test for smoking It is estimated that roughly half of smokers lie when asked about their smoking involvement. Pulse CO-oximeters may be a way to get information about smoking without relying on patients鈥� statements. Pulse CO-oximeters use light that shines through a fingernail, and it measures carbon monoxide in blood. These devices are used by firemen and emergency departments to detect carbon monoxide poisoning, but they can also be used to identify smokers. The accompanying table lists results from people aged 18鈥�44 when the pulse CO-oximeter is set to detect a 6% or higher level of carboxyhemoglobin (based on data from 鈥淐arbon Monoxide Test Can Be Used to Identify Smoker,鈥� by Patrice Wendling, Internal Medicine News, Vol. 40., No. 1, and Centers for Disease Control and Prevention).

CO-Oximetry Test for Smoking

Analyzing the Results

False Positive Based on the results in the table, find the probability that a subject is not a smoker, given that the test result is positive.

In Exercises 1鈥�10, use the data in the accompanying table and express all results in decimal form. (The data are from 鈥淢ortality Reduction with Air Bag and Seat Belt Use in Head-On Passenger Car Collisions,鈥� by Crandall, Olson, and Sklar, American Journal of Epidemiology, Vol. 153, No. 3.) Drivers Involved in Head-On Collision of Passenger Cars.

Drivers Involved in Head-On Collision of Passenger Cars

Seatbelt Use If one driver is randomly selected, find the probability he or she was using a seatbelt

New Jersey Lottery Let A denote the event of placing a $1 straight bet on the New Jersey Pick 3 lottery and winning. There are 1000 different ways that you can select the three digits (with repetition allowed) in this lottery, and only one of those three-digit numbers will be the winner. What is the value of? What is the value of$P\left(\stackrel{炉}{A}\right)$?

At Least One. In Exercises 5鈥�12, find the probability.

At Least One Correct Answer If you make random guesses for 10 multiple choice SAT test questions (each with five possible answers), what is the probability of getting at least 1 correct? If these questions are part of a practice test and an instructor says that you must get at least one correct answer before continuing, is there a good chance you will continue?

Black Cars Use subjective probability to estimate the probability of randomly selecting a car and getting one that is black.

In Exercises 5鈥�36, express all probabilities as fractions.

Scheduling Routes A presidential candidate plans to begin her campaign by visiting the capitals of 5 of the 50 states. If the five capitals are randomly selected without replacement, what is the probability that the route is Sacramento, Albany, Juneau, Hartford, and Bismarck, in that order?

At Least One. In Exercises 5鈥�12, find the probability.

At Least One Defective iPhone It has been reported that 20% of iPhones manufactured by Foxconn for a product launch did not meet Apple鈥檚 quality standards. An engineer needs at least one defective iPhone so she can try to identify the problem(s). If she randomly selects 15 iPhones from a very large batch, what is the probability that she will get at least 1 that is defective? Is that probability high enough so that she can be reasonably sure of getting a defect for her work?

In Exercises 9鈥�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.

Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order from 惭肠顿辞苍补濒诲鈥檚 or an order that is accurate. Are the events of selecting an order from 惭肠顿辞苍补濒诲鈥檚 and selecting an accurate order disjoint events?

At Least One. In Exercises 5鈥�12, find the probability.

Wi-Fi Based on a poll conducted through the e-edition of USA Today, 67% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among four randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond?