Name:______________________________________________________________________________Date:_______________Score:____/40
Units 4 and 5: Probability Rules Assessment Version B
Answer the following questions based on your knowledge of probability. All work must be shown—an answer
without supporting work will not receive credit. Be sure to clearly indicate your final answer. All probabilities
should be decimals rounded to the nearest ten thousandth.
1. Molly’s college offers two sections of Computer Science. From what she has heard about the two professors
listed, Molly estimates that her chances of passing the course are 0.8 if she gets Professor Smith and 0.6 if
she gets Professor Brown. The registrar uses a lottery to randomly assign the 120 enrolled students based
on the number of available seats in each class. There are 70 seats available in Professor Smith’s section and
50 available in Professor Brown’s section.
a. What is the probability that Molly with pass
Computer Science? (3 pts)
b. At the end of the semester, we find out that
Molly failed the course. What is the probability
that she had Professor Brown? (3 pts)
2. Of the members of the Spring Lake Bowling Lanes, 57% have a lifetime membership and bowl regularly (3
or more times per week). If 70% of the club members bowl regularly, find the probability that a randomly
selected member is a lifetime member, given that they bowl regularly. (3 pts)
3. A company’s human resources officer reports
a breakdown of employees by job type and
gender, as shown in the table. What is the
probability that a worker selected at random
is:
a. Female? (2 pts)
b. Female or a production worker? (2 pts)
c. Female, if the person works in production? (2
pts)
d. A production worker, if the person is female? (2
pts)
e. Do these data suggest that job type is independent of gender? Explain. (3 pts)
4. According to a recent Gallup survey, 93% of teens use the Internet, but there are differences in how teen
boys and girls say they use computers. The telephone poll found that 77% of boys had played computer
games in the past week, compared with 65% of girls. On the other hand 76% of girls said they had emailed
friends in the past week, compared with only 65% of boys.
a. For boys, the cited percentages are 77% playing
computer games and 65% using email. That
total is 142%, so there is obviously a mistake in
the report. No? Explain. (2 pts)
b. Based on these results, do you think emailing
and playing games are mutually exclusive?
Explain. (2 pts)
c. Do you think emailing friends and gender are
independent? Explain. (2 pts)
d. Suppose that in fact, 93% of teens in your area
do use the internet. You want to interview a
few who do not, so you start contacting
teenagers at random. What is the probability
that it takes you 5 interview until you find the
first person that does not use the internet? (3
pts)
5. A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a
dent, when they are delivered to car dealers. This same organization believes that 7% have a functional
defect—something does not work properly—and that 2% of new cars have both types of problems.
a. If you buy a new car, what is the probability
that it has a cosmetic defect but no functional
defect? (2 pts)
b. What is the probability it has some kind of
defect? (2 pts)
c. If you notice a dent on a new car, what is the
probability that it has a functional defect too?
(2 pts)
d. Are the two kinds of defects disjoint events?
Explain. (2 pts)
e. Are the two events independent? Explain. (3 pts)
Bonus: (up to 4 pts)
Suppose that 70% of the woman who suspect they may be pregnant purchase an in-home pregnancy test are
actually pregnant. Further suppose that the test is 98% accurate. What is the probability that woman whose test
indicates that she is pregnant actually is?