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Chapter 5: Q. 53 (page 329)
Union and intersection Suppose A and B are two events such that P (A), P (B), and
P (A鈭狟). Find P (A鈭〣).
The Pis.
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Suppose that a student is randomly selected from a large high school. The probability
that the student is a senior is The probability that the student has a driver鈥檚 license
is . If the probability that the student is a senior or has a driver鈥檚 license is ,
what is the probability that the student is a senior and has a driver鈥檚 license?
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.
Three pointers The figure shows the results of a basketball player attempting many
point shots. Explain what this graph tells you about chance behavior in the short run and
long run.
Which one of the following is true about the events 鈥淥wner has a Chevy鈥� and
鈥淥wner鈥檚 truck has four-wheel drive鈥�?
a. These two events are mutually exclusive and independent.
b. These two events are mutually exclusive, but not independent.
c. These two events are not mutually exclusive, but they are independent.
d. These two events are neither mutually exclusive nor independent.
e. These two events are mutually exclusive, but we do not have enough information to determine if they are independent.
Get rich A survey of 4826 randomly selected young adults (aged ) asked, 鈥淲hat do you think are the chances you will have much more than a middle-class income at age ?鈥� The two-way table summarizes the responses.
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance.
a. Find . Interpret this value in context.
b. Given that the chosen survey respondent didn鈥檛 say 鈥渁lmost no chance,鈥� what鈥檚 the probability that this person is female? Write your answer as a probability statement using correct symbols for the events.
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