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Chapter 7—Basic Concepts of Probability
MULTIPLE CHOICE QUESTIONS
7.1 Which of the following is NOT an appropriate use of probability?
7.2 + Where is “subjective probability” most likely to be invoked?
7.3 + A frequentistic approach to probability is likely to be invoked
7.4 Which of the following is NOT a way of setting probabilities?
7.5 Of 50 women treated for breast cancer in the local cancer unit, 35 of them
survived for at least 5 years. For a woman who has just been diagnosed with
breast cancer, our best guess is that the probability that she will survive for 5
years is
7.6 + Out of a pool of 40 men and 10 women, all of whom are equally qualified for one
position as an instructor in chemistry, the person hired was a male. The
probability that this would happen if the department ignored gender as a variable
in selection is
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7.7 Last year there were 300 new Ph.D.s in chemistry looking for academic jobs. Of
those, 100 were women and 200 were men. Nationwide last year there were 75
new hirings in chemistry departments. How many of those new hires would be
expected to be women if there was no gender discrimination?
7.8 Following up on the preceding question, suppose that you found that 27 of the
new hires were women. You would probably be justified in concluding that
7.9 + I am looking down on a parking lot, and can see that about 10% of the cars are red
and about 15% of the cars are blue. To estimate the probability that the next car
to leave the lot will be red or blue, I would
d) It can’t be estimated from the information provided.
7.10 In the parking lot below me, 40% of the vehicles are silver, and about 25% of the
vehicles are pickup trucks. The probability that the next vehicle to leave the
parking lot will be a silver pickup is
7.11 To estimate that probability that the next vehicle to leave the parking lot will be a
silver pickup, we first need to
7.12 + Two events are mutually exclusive when
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7.13 An exhaustive set of events is one which
7.14 When we want to calculate the probability of the joint occurrence of two or more
independent events, we invoke
7.15 + Using an example from the text, when we calculate the probability that a
supermarket flier will be left among the canned goods if it contains a notice not to
litter, we will be dealing with
7.16 + Using the example from the text about the supermarket fliers, when we calculate
the probability that a flier will be left either among the canned goods or in the
bottom of the shopping cart, we need to invoke
7.17 Once again using the example about supermarket fliers, we would have evidence
that the “don’t litter” message on the flier was effective if we found that
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7.18 One difference between the additive and the multiplicative rules that helps us
remember when to use which is
7.19 + If I am interested in the probability that you will be depressed and that you will
have experienced a great deal of stress in the past month, I am talking about
7.20 If I am interested in the probability that you will be depressed if you have
experienced a great deal of stress in the past month, I am talking about
7.21 When we are talking about joint probabilities we are likely to invoke
7.22 The vertical bar “|” is read as _______ when we are talking about probabilities.
7.23 + I would like to calculate the probability that you will do well in this course if you
are a member of a group of students who study together. The most important
word in that last sentence is
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7.24 Two events are said to be independent if
7.25 A discrete variable is one that
7.26 A continuous variable is one that
7.27 + Which of the following is most likely to be a discrete variable?
7.28 For which kind of variable is the ordinate of a graph labeled as “density?”
7.29 + With continuous variables we
7.30 When we sample with replacement we
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7.31 + If I am drawing observations out of a hat while sampling with replacement, the
probability of drawing a certain outcome
7.32 Which of the following is NOT a joint probability?
7.33 + Which of the following events are most likely to be independent?
7.34 + If Brian has a 50% chance of getting a job, and that job would either be at IBM or
AT&T, what is the probability that he will soon be working at IBM?
7.35 Given a normal distribution of intelligence test scores (mean=100, s.d.=15), what
is the probability that someone will score between 100 and 115?
7.36 + The events most likely to be mutually exclusive are
7.37 If a set of events contains all of the possible outcomes, it is said to be
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7.38 p(getting a job | knowing the manager) is the notation for the probability of
7.39 We might find that 65% of women report themselves to be politically liberal,
while only 52% of men report that they are liberal. The proportions would be
described as
7.40 When two teams compete against each other, the result for Team A can be win,
draw, or lose. These events are
7.41 Two events are mutually exclusive if
TRUE/FALSE QUESTIONS
independent of the probability of rolling a 6 on the second roll.
strawberry, 10 orange, and 5 banana. The probability that the first candy pulled
out of the bag will be butterscotch or strawberry is .45.
.50.
that an event falls in a certain interval; and when observing a discrete variable,
you can calculate the probability of a specific outcome.
replacement.
election patterns is an example of the relative frequency view of probability.
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example of the subjective probability.
major, and the probability that a student in this class has red hair is .05, then the
joint probability of being a Psychology major and a red head in this class is .95.
7.50 [FALSE] The probability that a student is a Psychology major given that she is
female is an example of joint probability.
OPEN-ENDED QUESTIONS
7.52 Identify each of the following examples as the analytic, relative frequency, or
subjective view of probability based on the example of a brother and sister
playing scrabble:
a) If the brother and sister are equally matched, there is a .50 probability that each
will win the game.
b) If the sister won 3 of the last 4 games, the probability that she will win this one
is .75.
c) The brother believes there is an 80% chance that he will beat his sister this
time.
7.53 Explain why it is important to know if someone is sampling with or without
replacement when calculating the probability of multiple events.
7.54 Your friend plays the lottery every day. Since he has never won, he is convinced
that the odds that he will win next time are even better. From a probability
perspective, what is wrong with your friend’s logic?
7.55 A bag of 100 marbles contains 30 blue marbles, 25 green marbles, 25 mixed
green/blue marbles, and 20 clear marbles. Marbles are returned to the bag after
every draw.
a) What is the probability of selecting a blue marble?
b) What is the probability of selecting a blue or green marble?
c) What is the probability of selecting a marble that is not clear?
d) What is the probability of selecting a blue marble on the first draw and then a
clear marble on the second draw?
7.56 Imagine the same bag of marbles, but this time, marbles are NOT returned to the
bag after each draw.
a) What is the probability of drawing 3 clear marbles in 3 draws?
b) What is the probability of drawing a clear marble, then a green, and then a
clear?
c) What is the probability of not selecting any clear marbles in three draws?
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7.57 A safety agency was interested in whether penalties for talking on a cell phone
while driving reduce the probability that individuals will DO SO. They randomly
contacted 100 cell phone users. Fifty were from a state that had a law prohibiting
this behavior, and 50 were from a state that had no such law. The data follow:
Use Cell Phone
While Driving
Do Not Use Cell
Phone While
Driving
Total
Law
10
40
50
No Law
20
30
50
Total
30
70
100
a) Calculate the simple probability that someone uses a cell phone while driving.
b) Calculate the joint probability that someone is in a state without the law and
uses their cell phone while driving.
c) Calculate the probability that someone will use their cell phone while driving
given they live in state with the law.
7.58 If the average score on the Graduate Record Exam was 500 and the standard
deviation was 100, what is the probability that a random student would score
between 400 and 600?
7.59 A kindergarten teacher assigns chores to her students on a weekly basis. One
student works on each task, and each student is assigned only one task a week.
During the first week of school, there were 20 students and 7 tasks. Also, 4 of the
students had brown hair.
a) What is the probability that a student would not be assigned a chore?
b) What is the probability that a student had brown hair?
c) What is the probability that a student had brown hair or had a chore?
d) What is the probability that a student had brown hair and a chore?
7.60 A local private school is selling raffle tickets for a new sports car. They plan to
sell 10,000 tickets.
a) What is the probability that you will win if you bought 1 ticket?
b) How many tickets are needed to have a .25 probability of winning?
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7.61 A professor rated how frequently students actively participated in class and then
calculated the probability of getting various grades broken down by participation.
The data follow:
A
B
C
D
F
Frequently
.06
.20
.03
.01
.00
Sometimes
.03
.12
.20
.03
.02
Rarely/Never
.01
.08
.07
.06
.08
a) What is the simple probability of getting an A?
b) What is the probability of getting an A given the student participated
frequently?
c) What is the simple probability of failing?
d) What is the probability of failing given the student participated rarely/never?
Answers to Open-ended Questions
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