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Chapter 5: Q 67. (page 332)
Tall people and basketball players Select an adult at random. Define events T: person is over feet tall, and
B: person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.
The correct order is
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Checking independence Suppose C and D are two events such that
and Are events C and D independent? Justify your answer.
Airport securityThe Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 辫补蝉蝉别苍驳别谤蝉鈥�in first class and in coach class. Some passengers were surprised when none of the passengers chosen for screening were seated in first class. We want to perform a simulation to estimate the probability that no first-class passengers would be chosen in a truly random selection.
a. Describe how you would use a table of random digits to carry out this simulation.
b. Perform one trial of the simulation using the random digits that follow. Copy the digits onto your paper and mark directly on or above them so that someone can follow what you did.
c. In of the trials of the simulation, none of the passengers chosen was seated in first class. Does this result provide convincing evidence that the TSA officers did not carry out a truly random selection? Explain your answer.
The two-way table summarizes data on whether students at a certain high school eat
regularly in the school cafeteria by grade level.
a. If you choose a student at random, what is the probability that the student eats
regularly in the cafeteria and is not a grader?
b. If you choose a student at random who eats regularly in the cafeteria, what is the probability that the student is a grader?
c. Are the events 鈥�grader鈥� and 鈥渆ats regularly in the cafeteria鈥� independent?
Justify your answer.
Teachers and college degrees Select an adult at random. Define events D: person has earned a college degree, and T: person鈥檚 career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.
Colorful disksA jar contains disks: each of four colors鈥攔ed, green, blue, and Page Number: yellow. Each set of disks of the same color is numbered from to . Suppose you draw one disk at random from the jar. Define events : get a red disk, and : get a disk with the number .
a. Make a two-way table that describes the sample space in terms of events and .
b. Find and .
c. Describe the event 鈥�and 鈥� in words. Then find the probability of this event.
d. Explain why Then use the general addition rule to compute
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