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Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 5: Probability in our Daily Lives
Statistics: The Art and
Science of Learning from
Data
Second Edition
by Agresti/Franklin
5.1.1) True or False: A truly random sequence of
rolling a dice will have occurrences of getting the
same number six times in a row.
a) True
b) False
Copyright © 2009 Pearson Education
5.1.1) True or False: A truly random sequence of
rolling a dice will have occurrences of getting the
same number six times in a row.
a) True
b) False
Copyright © 2009 Pearson Education
5.1.2) Flip a coin and record the number of times it
lands “heads up”. When would you expect the
proportion of “heads” to be 0.5, . . .
a)
b)
c)
d)
e)
After 1 flip
After 50 flips
After 100 flips
After 500 flips
None of the above
Copyright © 2009 Pearson Education
5.1.2) Flip a coin and record the number of times it
lands “heads up”. When would you expect the
proportion of “heads” to be 0.5, . . .
a)
b)
c)
d)
e)
After 1 flip
After 50 flips
After 100 flips
After 500 flips
None of the above
Copyright © 2009 Pearson Education
5.1.3) If we wanted to determine the success
probability of a manned spaceship successfully
reaching Mars, we would need to use…
a) The relative frequency definition of probability.
b) The subjective definition of probability.
Copyright © 2009 Pearson Education
5.1.3) If we wanted to determine the success
probability of a manned spaceship successfully
reaching Mars, we would need to use…
a) The relative frequency definition of probability.
b) The subjective definition of probability.
Copyright © 2009 Pearson Education
5.1.4) Which of the following events are NOT
independent?
1: Getting a “3” on the first roll of a die.
2: Getting a “3” on the second roll of a die.
3: Rolling an odd number on the first roll of a die.
a)
b)
c)
d)
1 and 2
1 and 3
2 and 3
All of the above are independent.
Copyright © 2009 Pearson Education
5.1.4) Which of the following events are NOT
independent?
1: Getting a “3” on the first roll of a die.
2: Getting a “3” on the second roll of a die.
3: Rolling an odd number on the first roll of a die.
a)
b)
c)
d)
1 and 2
1 and 3
2 and 3
All of the above are independent.
Copyright © 2009 Pearson Education
5.1.5) True or False: If your friend rolls a six sided
dice and gets a “1” eight times the probability that
she will roll a “1” on the 9th roll is less than 1/6.
a) True
b) False
Copyright © 2009 Pearson Education
5.1.5) True or False: If your friend rolls a six sided
dice and gets a “1” eight times the probability that
she will roll a “1” on the 9th roll is less than 1/6.
a) True
b) False
Copyright © 2009 Pearson Education
5.1.6) True or False: A random sample of 20
college students had 19 Republicans, therefore,
the probability of randomly selecting a Republican
college student from the entire student body is
exactly 0.95.
a) True
b) False
Copyright © 2009 Pearson Education
5.1.6) True or False: A random sample of 20
college students had 19 Republicans, therefore,
the probability of randomly selecting a Republican
college student from the entire student body is
exactly 0.95.
a) True
b) False
Copyright © 2009 Pearson Education
5.2.1) True or False: If the probability that it rains
today is 0.4 and the probability that it rains
tomorrow is 0.7, the probability that it rains both
days is 1.1.
a) True
b) False
Copyright © 2009 Pearson Education
5.2.1) True or False: If the probability that it rains
today is 0.4 and the probability that it rains
tomorrow is 0.7, the probability that it rains both
days is 1.1.
a) True
b) False
Copyright © 2009 Pearson Education
5.2.2) Suppose that you pass through three traffic
lights on your way to school everyday and you
record the total number of times that you are
stopped by a red light. What is the sample space?
Let S = stopped by a light and N = not stopped by
a light.
a) S= {S, N}
b) S= {SSS, SNS, NSS, SSN, NNS, NSN, SNN,
NNN}
c) S= {1,2,3}
d) S= {0,1,2,3}
Copyright © 2009 Pearson Education
5.2.2) Suppose that you pass through three traffic
lights on your way to school everyday and you
record the total number of times that you are
stopped by a red light. What is the sample space?
Let S = stopped by a light and N = not stopped by
a light.
a) S= {S, N}
b) S= {SSS, SNS, NSS, SSN, NNS, NSN, SNN,
NNN}
c) S= {1,2,3}
d) S= {0,1,2,3}
Copyright © 2009 Pearson Education
5.2.3) Suppose a student is totally unprepared for
a five question true or false test and has to guess
for every question. Getting one question correct is
independent of getting another question correct.
What is the probability that she guessed all five of
them correctly?
a)
b)
c)
d)
e)
0
0.03
0.10
0.50
0.97
Copyright © 2009 Pearson Education
5.2.3) Suppose a student is totally unprepared for
a five question true or false test and has to guess
for every question. Getting one question correct is
independent of getting another question correct.
What is the probability that she guessed all five of
them correctly?
a)
b)
c)
d)
e)
0
0.03
0.10
0.50
0.97
Copyright © 2009 Pearson Education
5.2.4) Suppose a student is totally unprepared for
a three question true or false test and has to guess
on every question. Getting one question correct is
independent of getting another question correct.
Using a tree diagram, what is the probability that
she guessed at least one of them correctly?
a)
b)
c)
d)
e)
0.125
0.33
0.66
0.875
0.97
Copyright © 2009 Pearson Education
5.2.4) Suppose a student is totally unprepared for
a three question true or false test and has to guess
on every question. Getting one question correct is
independent of getting another question correct.
Using a tree diagram, what is the probability that
she guessed at least one of them correctly?
a)
b)
c)
d)
e)
0.125
0.33
0.66
0.875
0.97
Copyright © 2009 Pearson Education
5.2.5) Does the gender of a person tend to effect whether
they agree with the statement “I would rather suffer than
watch someone I love suffer”? Let M = male, F = female,
and A = agree strongly with the statement. For the 2004
GSS data, how could you check to see if M and A are
independent?
a)
b)
c)
d)
Male
Female
Agree Strongly
438
399
Disagree Strongly
3
7
Check to see if P(A)P(M) = P(A and M)
Check to see if P(A) = P(M)
Check to see if P(A and M) = P(A) + P(M)
Check to see if P(M) = P(A and M)
Copyright © 2009 Pearson Education
5.2.5) Does the gender of a person tend to effect whether
they agree with the statement “I would rather suffer than
watch someone I love suffer”? Let M = male, F = female,
and A = agree strongly with the statement. For the 2004
GSS data, how could you check to see if M and A are
independent?
a)
b)
c)
d)
Male
Female
Agree Strongly
438
399
Disagree Strongly
3
7
Check to see if P(A)P(M) = P(A and M)
Check to see if P(A) = P(M)
Check to see if P(A and M) = P(A) + P(M)
Check to see if P(M) = P(A and M)
Copyright © 2009 Pearson Education
5.3.1) Let P = a woman is pregnant and let POS = a
pregnancy test indicates a woman is pregnant. A
pregnancy test will accurately indicate that a pregnant
woman IS pregnant 99% of the time. Use the events
defined above to identify the probability stated above.
a)
b)
c)
d)
P(P)
P(POS)
P(P | POS)
P(POS | P)
Copyright © 2009 Pearson Education
5.3.1) Let P = a woman is pregnant and let POS = a
pregnancy test indicates a woman is pregnant. A
pregnancy test will accurately indicate that a pregnant
woman IS pregnant 99% of the time. Use the events
defined above to identify the probability stated above.
a)
b)
c)
d)
P(P)
P(POS)
P(P | POS)
P(POS | P)
Copyright © 2009 Pearson Education
5.3.2) Let P = a women is pregnant and let POS = a
pregnancy test indicates a women is pregnant. It is
possible for a pregnancy test to give a false positive
if she uses the test too early. Suppose that there is a
33% probability that the test gives a positive
indication when the women is not actually pregnant.
Use the events defined above to identify the
probability stated above.
a)
b)
c)
d)
P(PC)
P(P C| POS)
P(POS | PC)
P(POS C | PC)
Copyright © 2009 Pearson Education
5.3.2) Let P = a women is pregnant and let POS = a
pregnancy test indicates a women is pregnant. It is
possible for a pregnancy test to give a false positive
if she uses the test too early. Suppose that there is a
33% probability that the test gives a positive
indication when the women is not actually pregnant.
Use the events defined above to identify the
probability stated above.
a)
b)
c)
d)
P(PC)
P(P C| POS)
P(POS | PC)
P(POS C | PC)
Copyright © 2009 Pearson Education
5.3.3) In 2006 the General Social Survey asked
participants if they thought it was “ok” for a woman to get
an abortion for any reason and also asked them for their
political party affiliation. Using the table below, what is the
probability of someone being opposed to a woman having
an abortion for any reason given that they are a strong
Republican?
Yes, “ok”
a)
b)
c)
d)
e)
Strong Democrat
0.05
Independent
0.22
Strong Republican
0.28
0.54
None of the above
Copyright © 2009 Pearson Education
No
145
123
128
282
46
162
5.3.3) In 2006 the General Social Survey asked
participants if they thought it was “ok” for a woman to get
an abortion for any reason and also asked them for their
political party affiliation. Using the table below, what is the
probability of someone being opposed to a woman having
an abortion for any reason given that they are a strong
Republican?
Yes, “ok”
a)
b)
c)
d)
e)
Strong Democrat
0.05
Independent
0.22
Strong Republican
0.28
0.54
None of the above
Copyright © 2009 Pearson Education
No
145
123
128
282
46
162
5.3.4) In 2006 the General Social Survey asked
participants if they thought it was “ok” for a woman to get
an abortion for any reason and also asked them for their
political party affiliation. Using the table below, what is the
probability that someone is a Strong Republican given
that they support a woman getting an abortion for any
reason?
Yes, “ok” No
Strong Democrat
a)
b)
c)
d)
e)
Independent
0.14
Strong Republican
0.22
0.28
0.54
None of the above
Copyright © 2009 Pearson Education
145
123
128
282
46
162
5.3.4) In 2006 the General Social Survey asked
participants if they thought it was “ok” for a woman to get
an abortion for any reason and also asked them for their
political party affiliation. Using the table below, what is the
probability that someone is a Strong Republican given
that they support a woman getting an abortion for any
reason?
Yes, “ok” No
Strong Democrat
a)
b)
c)
d)
e)
Independent
0.14
Strong Republican
0.22
0.28
0.54
None of the above
Copyright © 2009 Pearson Education
145
123
128
282
46
162
5.3.5) In 2006, the General Social Survey asked
participants if they thought it was o.k. for a women to get
an abortion for any reason and asked them for their
political party affiliation. Using the table below, are the
events being a Strong Republican (R) and supporting a
women getting an abortion for any reason (Y)
independent events?
Yes
No
a)
b)
c)
d)
Yes, P(R) = P(R|Y).
Yes, P(Y) = P(R|Y).
No, P(Y) ≠ P(R|Y).
No, P(R) ≠ P(R|Y).
Strong Democrat
145
123
Independent
128
282
Strong Republican
46
162
Copyright © 2009 Pearson Education
5.3.5) In 2006, the General Social Survey asked
participants if they thought it was o.k. for a women to get
an abortion for any reason and asked them for their
political party affiliation. Using the table below, are the
events being a Strong Republican (R) and supporting a
women getting an abortion for any reason (Y)
independent events?
Yes
No
a)
b)
c)
d)
Yes, P(R) = P(R|Y).
Yes, P(Y) = P(R|Y).
No, P(Y) ≠ P(R|Y).
No, P(R) ≠ P(R|Y).
Strong Democrat
145
123
Independent
128
282
Strong Republican
46
162
Copyright © 2009 Pearson Education
5.4.1) Suppose that in order for a particular electrical
circuit to function all of its 10 parts must work. Each of
the parts works independently of each other. The
probability that each of the parts works is 99%. What
is the probability at least one of the parts fails and
thus the circuit fails?
a)
b)
c)
d)
e)
Almost Zero
0.01
0.096
0.99
Almost One
Copyright © 2009 Pearson Education
5.4.1) Suppose that in order for a particular electrical
circuit to function all of its 10 parts must work. Each of
the parts works independently of each other. The
probability that each of the parts works is 99%. What
is the probability at least one of the parts fails and
thus the circuit fails?
a)
b)
c)
d)
e)
Almost Zero
0.01
0.096
0.99
Almost One
Copyright © 2009 Pearson Education
5.4.2) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time
and accurately indicates that a woman wasn’t
pregnant (-) 99.2% of the time. What is the
probability that the test gives a positive (+) reading
and the woman is pregnant?
a)
b)
c)
d)
e)
0.99
0.55
0.5445
0.4955
0.0055
Copyright © 2009 Pearson Education
5.4.2) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time
and accurately indicates that a woman wasn’t
pregnant (-) 99.2% of the time. What is the
probability that the test gives a positive (+) reading
and the woman is pregnant?
a)
b)
c)
d)
e)
0.99
0.55
0.5445
0.4955
0.0055
Copyright © 2009 Pearson Education
5.4.3) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time and
accurately indicates that a woman wasn’t pregnant
(-) 99.2% of the time. What is the probability that the
test gives a positive (+) reading and the woman is
not pregnant?
a)
b)
c)
d)
e)
0.5445
0.45
0.01
0.0055
0.0036
Copyright © 2009 Pearson Education
5.4.3) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time and
accurately indicates that a woman wasn’t pregnant
(-) 99.2% of the time. What is the probability that the
test gives a positive (+) reading and the woman is
not pregnant?
a)
b)
c)
d)
e)
0.5445
0.45
0.01
0.0055
0.0036
Copyright © 2009 Pearson Education
5.4.4) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time
and accurately indicates that a woman wasn’t
pregnant (-) 99.2% of the time. What is the
probability that the test gives a positive (+)
reading?
a)
b)
c)
d)
e)
0.4519
0.5481
0.55
0.992
0.99
Copyright © 2009 Pearson Education
5.4.4) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time
and accurately indicates that a woman wasn’t
pregnant (-) 99.2% of the time. What is the
probability that the test gives a positive (+)
reading?
a)
b)
c)
d)
e)
0.4519
0.5481
0.55
0.992
0.99
Copyright © 2009 Pearson Education
5.4.5) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time
and accurately indicates that a woman wasn’t
pregnant (-) 99.2% of the time. What is the
probability someone who gets a positive (+)
reading really is pregnant?
a)
b)
c)
d)
e)
0.55
0.9045
0.99
0.992
0.9934
Copyright © 2009 Pearson Education
5.4.5) Suppose that 55% of all women that use a
pregnancy test really are pregnant. Additionally,
suppose that a pregnancy test accurately indicates
that a woman was pregnant (+) 99% of the time
and accurately indicates that a woman wasn’t
pregnant (-) 99.2% of the time. What is the
probability someone who gets a positive (+)
reading really is pregnant?
a)
b)
c)
d)
e)
0.55
0.9045
0.99
0.992
0.9934
Copyright © 2009 Pearson Education