Name_________________
Chapter 14 & 15
Probability Rules & Examples
For each of the following questions:
1) Make a Venn Diagram, table, or tree diagram for each question.
2) Write the rule using formula notation for each part
3) Find each probability for each part
1) Suppose that 40% of cars in your city are manufactured in the United States, 30% in Japan, 10% in
Germany and 20% in other countries. If cars are selected at random, find the probability that:
a. A car is not U.S. made
b. It is made in Japan or Germany
c. Driving down the road, you see two in a row from Japan.
d. None three cars come from Germany
e. At least one of three cars is U.S. made.
f. The first Japanese car is the fourth one you choose.
2) For each of the following, use a deck of 52 cards to find the probability of each situation.
A) One card is drawn. What is the probability it is an ace or red?
B) Two cards are drawn without replacement. What is the probability they are both aces?
C) Three cards are drawn without replacement. What is the probability they are all red cards?
D) Three cards are drawn without replacement. What is the probability they are all spades?
E) Four cards are drawn without replacement. What is the probability they are all facecards (J,Q,K)?
F) I draw one card and look at it. I tell you it is red. What is the probability it is a heart? And what is
the probability it is red, given that it is a heart?
G) Are Red card and Spade independent? Mutually Exclusive?
H) Are Red card and Ace independent? Mutually Exclusive?
I) Are face card and King independent? Mutually Exclusive?
3) A survey of students found that 56% live in a campus residence hall, 62% participate in a campus meal
program, and 42% do both.
A) Draw a Venn diagram to represent the situation.
B) What’s the probability that a randomly selected student either lives or eats on campus.
C) What’s the probability that a randomly selected student lives off campus and doesn’t have a meal
program?
D) What’s the probability that a randomly selected student lives in a residence hall but doesn’t have a
meal program?
E) While dining in a campus facility open only to students with meal plans, you meet someone
interesting. What is the probability that your new acquaintance lives on campus?
F) Are living on campus and having a meal plan independent? Are they disjoint?
4) Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a
blood test and 22% receive both tests.
A) Draw a Venn diagram to represent the situation
B) What is the probability that a randomly selected DWI suspect is given a test?
C) What is the probability that a randomly selected DWI suspect is given a blood test or a breath test,
but not both?
D) What is the probability that a randomly selected DWI suspect is given neither test?
E) Complete the following table for DWI suspects.
Breath Test
Yes
Blood Test
No
Total
Yes
No
Total
F) Are giving a DWI suspect a blood test and a breath test mutually exclusive?
G) Are giving the two tests independent?
5) The following table shows the number of males and females wearing Jeans one day in class. Find the
following probabilities:
Jeans
Other
Total
Male
12
5
17
Female
8
11
19
Total
20
16
36
A)
B)
C)
D)
What is the probability that a male wears jeans?
What is the probability that someone wearing jeans is a male?
Are being male and wearing jeans disjoint?
Are gender and attire independent?
6) In April 2003, Science Magazine reported on a new computer based test for ovarian cancer, “clinical
proteomics,” that examines a blood sample for the presence of certain patterns of proteins. Ovarian
cancer, though dangerous, is very rare, afflicting only 1 of every 5000 women. The test is highly
sensitive, able to correctly detect the presence of ovarian cancer in 99.97% of women who have the
disease. However, it is unlikely to be used as a screening test in the general population because the
test gave false positives 5% of the time. Why are false positives such a big problem? Draw a tree
diagram and determine the probability that a woman who tests positive using this method actually has
ovarian cancer.
7) For men, binge drinking is defined as having five or more drinks in a row, and for women as having four
or more drinks in a row. According to a study, 44% of college students engage in binge drinking, 37%
drink moderately, and 19% abstain entirely. Another study found that among binge drinkers, 17% have
been involved in an alcohol-related accident, while among non-binge drinkers only 9% have been
involved in an alcohol-related car accident.
a. Make a tree diagram to represent the situation
b. What’s the probability that a randomly selected college student will be a binge drinker who has
had an alcohol-related car accident?
c. What is the probability of having an alcohol related accident and not being a binge drinker?
d. What is the probability of abstaining and having an alcohol-related accident?
e. What is the probability that a selected student has an alcohol-related accident?
f. What is the probability that a selected student has not had an alcohol-related accident?
8) A recent Maryland highway safety study found that in 77% of all accidents the driver was wearing a
seatbelt. Accident reports indicated that 92% of those drivers escaped serious injury (defined as
hospitalization or death), but only 63% of the non-belted drivers were so fortunate.
a. Make a tree diagram to represent the situation
b. What the probability that a driver who was seriously injured wasn’t wearing a seatbelt?
c. What’s the probability that an accident involving a serious injury had a driver not wearing a
seatbelt?
d. What’s the probability that a driver involved in an accident was wearing their seat belt?