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Chapter 5: Q. 106. (page 337)
If P(A) = 0.24, P(B) = 0.52, and A and B are independent events, what is P(A or B)?
a.
b.
c.
d.
e. The answer cannot be determined from the information given.
The required answer is
The correct option is
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Will Luke pass the quiz ? Luke鈥檚 teacher has assigned each student in his class an online quiz, which is made up of multiple-choice questions with options each. Luke hasn鈥檛 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鈥檚 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.
Recycling Do most teens recycle? To find out, an AP庐 Statistics class asked an SRS of students at their school whether they regularly recycle. In the sample, students said that they recycle. Is this convincing evidence that more than half of the students at the school would say they regularly recycle? The dotplot shows the results of taking SRSS of students from a population in which the true proportion who recycle is .
a. Explain why the sample result (out of said "Yes") does not give convincing evidence that more than half of the school's students recycle.
b. Suppose instead that students in the class's sample had said "Yes." Explain why this result would give convincing evidence that a majority of the school's students recycle.
AARP, and Medicare (4.1) To find out what proportion of Americans support proposed
Medicare legislation to help pay medical costs, the AARP conducted a survey of their
members (people over age who pay membership dues). One of the questions was:
鈥淓ven if this plan won鈥檛 affect you personally either way, do you think it should be passed
so that people with low incomes or people with high drug costs can be helped?鈥� Of the
respondents, answered 鈥淵es.鈥�
a. Describe how undercoverage might lead to bias in this study. Explain the likely
direction of the bias.
b. Describe how the wording of the question might lead to bias in this study. Explain the
likely direction of the bias.
Middle school values Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data. 
Suppose we select one of these students at random. What鈥檚 the probability of each of the following?
a. The student is a sixth-grader or rated good grades as important.
b. The student is not a sixth-grader and did not rate good grades as important.
Does the new hire use drugs? Many employers require prospective employees to
take a drug test. A positive result on this test suggests that the prospective employee uses
illegal drugs. However, not all people who test positive use illegal drugs. The test result
could be a false positive. A negative test result could be a false negative if the person
really does use illegal drugs. Suppose that of prospective employees use drugs and
that the drug test has a false positive rate of and a false negative rate of.
Imagine choosing a prospective employee at random.
a. Draw a tree diagram to model this chance process.
b. Find the probability that the drug test result is positive.
c. If the prospective employee鈥檚 drug test result is positive, find the probability that she
or he uses illegal drugs.
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