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Chapter 5: Q. 99. (page 336)
Checking independence Suppose A and B are two events such that, and. Are events A and B independent? Justify your answer.
Events and are independent
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What is the probability that the person owns a Chevy, given that the truck has four-wheel drive?
Reading the paper In a large business hotel, 40% of guests read the Los Angeles Times. Only 25% read the Wall Street Journal. Five percent of guests read both papers. Suppose we select a hotel guest at random and record which of the two papers the person reads, if either. What’s the probability that the person reads the Los Angeles Times or the Wall Street Journal?
a. Make a Venn diagram to display the outcomes of this chance process using events L:reads the Los Angeles Times and W: reads the Wall Street Journal.
b. Find P.
Free-throw practice At the end of basketball practice, each player on the team must shoot free throws until he makes of them. Dwayne is a free-throw shooter. That is, his probability of making any free throw is . We want to design a simulation to estimate the probability that Dwayne make free throws in at most shots. Describe how you would use each of the following chance devices to perform one trial of the simulation.
a. Slips of paper
b. Random digits table
c. Random number generator
Will Luke pass the quiz ? Luke’s teacher has assigned each student in his class an online quiz, which is made up of multiple-choice questions with options each. Luke hasn’t been paying attention in class and has to guess on each question. However, his teacher allows each student to take the quiz three times and will record the highest of the three scores. A passing score is or more correct out of . We want to perform a simulation to estimate the score that Luke will earn on the quiz if he guesses at random on all the questions.
a. Describe how to use a random number generator to perform one trial of the simulation. The dotplot shows Luke’s simulated quiz score in trials of the simulation.
b. Explain what the dot at represents.
c. Use the results of the simulation to estimate the probability that Luke passes the quiz.
d. Doug is in the same class and claims to understand some of the material. If he scored points on the quiz, is there convincing evidence that he understands some of the material? Explain your answer.
Preparing for the GMAT A company that offers courses to prepare students for the Graduate Management Admission Test (GMAT) has collected the following information about its customers: are undergraduate students in business, are undergraduate students in other fields of study, and are college graduates who are currently employed. Choose a customer at random.
a. What must be the probability that the customer is a college graduate who is not currently employed? Why?
b. Find the probability that the customer is currently an undergraduate. Which probability rule did you use to find the answer?
c. Find the probability that the customer is not an undergraduate business student. Which probability rule did you use to find the answer?
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