Chapter 4: Probability
Q8
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
Driver Killed | Driver Not killed | |
Seatbelt Used | 3655 | 7005 |
Seatbelt not Used | 4402 | 3040 |
Complement If A represents the event of randomly selecting one driver included in the table and getting someone who was using a seatbelt, what does represent? Find the value of .
Q8
In Exercises 6鈥10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.
Developed Flu | Did not develop Flu | |
Vaccine Treatment | 14 | 1056 |
Placebo | 95 | 437 |
if 1 of the 1602 subjects is randomly selected, find the probability of getting 1 who had the vaccine treatment and developed flu.
Q8
At Least One. In Exercises 5鈥12, find the probability.
Births in China In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in 2015.)
Q8
In Exercises 5鈥36, express all probabilities as fractions.
Soccer Shootout In soccer, a tie at the end of regulation time leads to a shootout by three members from each team. How many ways can 3 players be selected from 11 players available? For 3 selected players, how many ways can they be designated as first, second, and third
Q8
Births Example 2 in this section includes the sample space for genders from three births. Identify the sample space for the genders from two births.
Q8
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-oximeters 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
Positive Test Results | Negative Test Results | |
Smoker | 49 | 57 |
Non-smoker | 24 | 370 |
Negative Predictive Value Find the negative predictive value of the test by finding the probability that the subject does not smoke, given that the test yields a negative result..
Q9
At Least One. In Exercises 5鈥12, find the probability.
Phone Survey Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0
Q9
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
Driver Killed | Driver Not killed | |
Seatbelt Used | 3655 | 7005 |
Seatbelt not Used | 4402 | 3040 |
Complement If A represents the event of randomly selecting one driver included in the table and getting someone who was not killed, what does represent? Find the value of .
Q9
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.
惭肠顿辞苍补濒诲鈥檚 | Burger King | 奥别苍诲测鈥檚 | 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 food that is not from 惭肠顿辞苍补濒诲鈥檚.
Q9
In Exercises 6鈥10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.
Developed Flu | Did not develop Flu | |
Vaccine Treatment | 14 | 1056 |
Placebo | 95 | 437 |
Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.