|AP Statistics Name: _____________________________________
Section 5.3 Day 1 Practice
1. In 1912 the luxury liner Titanic, on its first voyage across the Atlantic, struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who lived and who died, by class of travel. Suppose we choose an adult passenger at random.
a) Given that the person selected was in first class, what’s the probability that he or she survived?
b) Correct Answer
0.3656. 36.56% of grades are lower than a B.
If the person selected survived, what’s the probability that he or she was a third-class passenger?
2. A computer company makes desktop and laptop computers at factories in three states—California, Texas, and New York. The California factory produces 40% of the company’s computers, the Texas factory makes 25%, and the remaining 35% are manufactured in New York. Of the computers made in California, 75% are laptops. Of those made in Texas and New York, 70% and 50%, respectively, are laptops. All computers are first shipped to a distribution center in Missouri before being sent out to stores. Suppose we select a computer at random from the distribution center.
a) Construct a tree diagram to represent this situation.
b) Correct Answer
Here is a tree diagram.
Find the probability that the computer is a laptop. Show your work.
c) Given that a laptop is selected, what is the probability that it was made in California?
3. Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in a recent year:
a) What is the probability that a randomly chosen return shows an adjusted gross income of $50,000 or more?
b) Given that a return shows an income of at least $50,000, what is the conditional probability that the income is at least $100,000?
4. The Kaiser Family Foundation recently released a study about the influence of media in the lives of young people aged 8–18 (www.kff.org/entmedia/mh012010pkg.cfm). In the study, 17% of the youth were classified as light media users, 62% were classified as moderate media users, and 21% were classified as heavy media users. Of the light users who responded, 74% described their grades as good (A’s and B’s), while only 68% of the moderate users and 52% of the heavy users described their grades as good. Suppose that we selected one young person at random.
a) Draw a tree diagram to represent this situation.
b) Find the probability that this person describes his or her grades as good.
c) Given that this person describes his or her grades as good, what is the probability that he or she is a heavy user of media?
5. Officials at Dipstick College are interested in the relationship between participation in (interscholastic) sports and graduation rate. The following table summarizes the probabilities of several events when a male Dipstick student is randomly selected.
Student participates in sports 0.20
Student participates in sports and graduates 0.18
Student graduates, given no participation in sports 0.82
a) Find the probability that a student graduates, given that he participates in sports.
b) Find the probability that the individual does not graduate, given that he participates in sports.
c) Draw a tree diagram to summarize the given probabilities and those you determined above.
d) Find the probability that the individual does not participate in sports, given that he graduates.