Math 171
Exam 2 Review Problems
The exam will have 10 problems. You will have the whole class
period to do the exam.
One problem on the exam will be very similar to a problem on the first
exam.
Working on the following problems will help you to prepare for the
exam. Be sure you can do all the assigned homework problems too!

1. A box has 2 red chips, 2 blue chips, and 1 green chip. Two chips
are randomly selected together.
a. List the elements in the sample space.
b. What is the probability of selecting 2 blue chips?
2. An experiment consists of tossing two ordinary dice and adding the
two numbers. Determine the probability of obtaining:
a. A sum of 8.
b. A sum less than or equal to 4.
3. If a person is randomly selected from the U.S. population, the odds
the person lives in California are 1 to 8.
a. What is the probability to two decimal places of a randomly
chosen person being from California?
b. What are the odds of a randomly chosen person not being
from California?
4. The digits 0 through 9 are written on slips of paper. An experiment
consists of randomly selecting one numbered slip of paper.
Determine the probability of each event in a, b, and c.
E: obtaining a prime number
F: obtaining a number divisible by 4
G: obtaining an odd number.
a. P(E  G)
b. P(E  F)
c. P(F  G)
d. Are events E and G independent? Explain why or why not.
5. A disc-shaped spinner has five sections with the following colors
and central angles:
Blue, 60˚; Red, 120˚; Green, 45˚; Red, 45˚; Yellow, 90˚.
Determine the following probabilities for one spin of the spinner.
a. P(Blue  Green)
b. P(Blue) + P(Green)
c. P(Red)
d. P(Red  Yellow)
6. Draw a probability tree showing the different outcomes and
probabilities for first spinning spinner A and then spinning Spinner
B.
A
B
7. A box contains 7 red marbles and 3 blue marbles. An experiment
consists of randomly selecting 2 marbles. Determine the
probability of obtaining 2 red marbles if:
a. The first marble selected is returned to the box before the
second marble is selected.
b. The first marble selected is not returned to the box for the
selection of the second marble.
8. A box contains five slips of paper numbered from 1 to 5. An
experiment consists of randomly selecting a slip of paper and then
rolling an ordinary die with numbers from 1 to 6. Determine the
following probabilities.
a. Selecting the number 3 and rolling a 3.
b. Selecting a number less than 4 and rolling a number less than
4.
c. Not selecting an odd number and not rolling a 6.
9. A radio station staff writes the phone numbers of eight finalists on
separate slips of paper and places them in a hat. Two phone
numbers are from listeners in the rural region, 2 phone numbers
are from listeners in the suburbs, and 4 phone numbers are from
city listeners. An experiment consists of randomly selecting one
slip of paper from the eight slips in the hat. If the experiment is
carried out three times, replacing the number drawn each time for
the next drawing, what is the probability of:
a. All three slips containing city phone numbers.
b. None of the slips containing the phone number of a listener
from the suburbs.
10. An ordinary die is tossed four times. What is the probability of
obtaining a number greater than 4 at least once?
11. A state lottery has a daily drawing to form a four-digit number.
The digits 1 through 9 are randomly selected for each of the four
digits. For each selection any one of the digits 1 through 9 is
possible. What is the probability to the nearest hundredth of the
four-digit number having at least one 3?
12. A teacher on her way to work passes through three stoplights
each morning. The distances between the stoplights are great and
the lights operate independently of each other. If the probabilities
of a red light are .4, .8, and .6 respectively, for each light, what is
the probability to the nearest hundredth that she will not have any
red lights on her way to work?
13. The data in the following table was obtained from the driving
records for a one-year period of 1108 randomly selected drivers.
Determine the probability to the nearest hundredth of each event
below by assuming that one of the 1108 drivers is randomly
selected.
Accident
No Acident
Total
Under 25
Years Old
60
278
338
Over 25
Years Old
8
762
770
Total
68
1040
1108
a. E: Driver was over 25 years old and had no accidents.
b. F: Driver was under 25 years old and had an accident.
c. G: Driver is under 25 years old or had an accident.
14. Is it possible for the probability of some event to be 1.5?
Explain.