Basic Probability
Name______________________________
1. Consider the chance experiment in which the type of transmission [automatic (A) or manual (M)] is recorded for
each of the next two cars purchased from a certain dealer.
a. Display the possible outcomes in a tree diagram.
b. List the sample space.
c. List the outcomes in the following events.
B = the event that at least one car has an automatic transmission.
C = the event that exactly one car as an automatic transmission
d. What are the outcomes in the event BC?
e. What are the outcomes in the event BC?
2. A family consisting of three people (Ann, Bill, and Chris) belongs to a medical clinic that always has a physician at
each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic exactly once and is
randomly assigned to a station. One experimental outcome is (1,2,1), which means that Ann was assigned to
station 1, Bill to station 2 and Chris to station 1.
a. List the sample space.
b. List all outcomes in the event A, that all three people go to the same station.
c. List all outcomes in the event B, that all three people go to different stations.
d. List all outcomes in the event C, that no one goes to station 2.
e. Identify outcomes in each of the following events:
𝐵̅ = ___________________________________________________________
𝐶̅ = ___________________________________________________________
A  B = ________________________________________________________
A  B = ________________________________________________________
A  C = ________________________________________________________
3. A four-sided die has faces with 1, 2, 3, and 4, spots.
a. List the sample space for rolling the die twice.
b. What is the probability of getting a sum of 5?
4. Imagine tossing a fair coin 3 times.
a. What is the sample space?
b. What is the probability of getting more heads than tails?
5. Choose a young adult (aged 25-29) at random. The probability is 0.13 that the person chosen did not complete
high school, 0.29 that the person has a high school diploma but no further education, and 0.30 that the person
has at least a bachelor’s degree.
a. What must be the probability that a randomly chosen young adult has some education beyond high school
but does not have a bachelor’s degree? Why?
b. What is the probability that a randomly chosen young adult has at least a high school education?
c. What is the probability that the person did complete high school?
6. A company that offers courses to prepare students for the GMAT has the following information about its
customers: 20% are currently undergraduate students in business, 15% are undergraduate students in other
fields of study; 60% are college graduates who are currently employed; and 5% are college graduates who are not
employed. Choose a customer at random.
a. What’s the probability that the customer is a currently an undergraduate?
b. What’s the probability that the customer is not an undergraduate business student?
7. The two-way table below describes the members of the U.S. Senate in a recent year. If we choose a U. S. Senator
at random, what’s the probability that we choose
a. a Democrat
b. a female?
Democrat
Republican
Male Female
46 13
37 4
c. a female Democrat?
d. a female or a democrat?
8. A radio station that plays classical music has a “bu request” program each Saturday evening. The percentages of
requests for composers on a particular night are as follows:
Bach
5%
Suppose that one of these requests is randomly selected.
Beethoven
26%
a. What is the probability that the request is for one of the three B’s?
b. What is the probability that the request is not for one of the two S’s?
c. Neither Bach nor Wagner wrote any symphonies. What is the probability
that the request is for a composer who wrote at least one symphony?
Brahms
Dvorak
Mendelssohn
Mozart
Schubert
Schumann
Tchaikovsky
Wagner
9%
2%
3%
21%
12%
7%
14%
1%