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Chapter 6
Probability in Statistics
Active Learning
Questions
For use with classroom
response systems
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 1
An event is considered “significant” if its
probability is less than or equal to 0.05.
Is it significant to be dealt an ace when you are
dealt one card from a standard 52-card deck?
(There are four aces in the deck.)
a. Yes
b. No
Slide 6 - 2
An event is considered “significant” if its
probability is less than or equal to 0.05.
Is it significant to be dealt an ace when you are
dealt one card from a standard 52-card deck?
(There are four aces in the deck.)
a. Yes
b. No
Slide 6 - 3
An event is considered “significant” if its
probability is less than or equal to 0.05.
Muhammad Ali’s professional boxing record
included 56 wins and 5 losses. If one match is
selected at random, would it be considered
significant if the match selected were a loss?
a. Yes
b. No
Slide 6 - 4
An event is considered “significant” if its
probability is less than or equal to 0.05.
Muhammad Ali’s professional boxing record
included 56 wins and 5 losses. If one match is
selected at random, would it be considered
significant if the match selected were a loss?
a. Yes
b. No
Slide 6 - 5
The advertising for a cold remedy claimed that no other
cold remedy acted faster. In an experiment to compare
that remedy with another one, it did act faster on average,
but the result was not significant. What does this mean?
a. The difference was so small that it could have happened by
chance even if the remedies were equivalent.
b. The difference was so small that it could have happened by
chance even if the remedies were not equivalent.
c. The probability of the observed difference occurring by
chance if the two remedies are equivalent was less than
0.05.
d. The population mean response times are different, but the
samples didn’t show it.
Slide 6 - 6
The advertising for a cold remedy claimed that no other
cold remedy acted faster. In an experiment to compare
that remedy with another one, it did act faster on average,
but the result was not significant. What does this mean?
a. The difference was so small that it could have happened by
chance even if the remedies were equivalent.
b. The difference was so small that it could have happened by
chance even if the remedies were not equivalent.
c. The probability of the observed difference occurring by
chance if the two remedies are equivalent was less than
0.05.
d. The population mean response times are different, but the
samples didn’t show it.
Slide 6 - 7
A coin is tossed three times and HHT (heads,
heads, tails) is observed. Is this result an outcome
or an event?
a. Outcome
b.
Event
Slide 6 - 8
A coin is tossed three times and HHT (heads,
heads, tails) is observed. Is this result an outcome
or an event?
a. Outcome
b.
Event
Slide 6 - 9
Five electronic switches are tested at random from
a day’s production and one is found to be
defective. Is this observation an outcome or an
event?
a. Outcome
b.
Event
Slide 6 - 10
Five electronic switches are tested at random from
a day’s production and one is found to be
defective. Is this observation an outcome or an
event?
a. Outcome
b.
Event
Slide 6 - 11
If you flip a coin three times, the possible
outcomes are HHH, HHT, HTH, THH, HTT, THT,
TTH, TTT. What is the probability of getting at
least one head and at least one tail?
a.
2
 0.6
3
c.
2
 0.25
8
b.
1
 0.50
2
d.
6
 0.75
8
Slide 6 - 12
If you flip a coin three times, the possible
outcomes are HHH, HHT, HTH, THH, HTT, THT,
TTH, TTT. What is the probability of getting at
least one head and at least one tail?
a.
2
 0.6
3
c.
2
 0.25
8
b.
1
 0.50
2
d.
6
 0.75
8
Slide 6 - 13
From four men and two women, a committee is
formed by drawing three names out of a hat. What
is the probability that all three names drawn are
those of men?
a.
4
 0.16
25
c.
4
 0.2
20
b.
3
 0.50
6
d.
3
 0.15
20
Slide 6 - 14
From four men and two women, a committee is
formed by drawing three names out of a hat. What
is the probability that all three names drawn are
those of men?
a.
4
 0.16
25
c.
4
 0.2
20
b.
3
 0.50
6
d.
3
 0.15
20
Slide 6 - 15
A sample space has 5000 equally likely possible
outcomes, what is the probability of each one?
1
a.
 0.001
1000
1
c.
 0.0002
5000
b.
2500
 0.50
5000
d.
5000
1
5000
Slide 6 - 16
A sample space has 5000 equally likely possible
outcomes, what is the probability of each one?
1
a.
 0.001
1000
1
c.
 0.0002
5000
b.
2500
 0.50
5000
d.
5000
1
5000
Slide 6 - 17
A bag of marbles holds 5 red marbles, 6 green
marbles and 14 blue marbles. IF one marble is
drawn out, what is the probability that it is green?
a.
5
 0.2
25
c.
14
 0.56
25
b.
d.
6
 0.24
25
6
 0.3
20
Slide 6 - 18
A bag of marbles holds 5 red marbles, 6 green
marbles and 14 blue marbles. IF one marble is
drawn out, what is the probability that it is green?
a.
5
 0.2
25
c.
14
 0.56
25
b.
d.
6
 0.24
25
6
 0.3
20
Slide 6 - 19
A quarterback completes 67% of his passes, what
is the probability that he will not complete his next
pass?
a.
0.67
b.
0.33
c.
0.23
d.
0.76
Slide 6 - 20
A quarterback completes 67% of his passes, what
is the probability that he will not complete his next
pass?
a.
0.67
b.
0.33
c.
0.23
d.
0.76
Slide 6 - 21
Use the table to
answer the question.
If one person is
selected to win a
door prize, what is
the probability he/she
is not Danish?
a.
37
 0.153
242
c.
205
 0.847
242
Nationality
English
Norwegian
Danish
German
French
Italian
Frequency
42
73
37
26
13
51
b.
73
 0.302
242
d.
169
 0.698
242
Slide 6 - 22
Use the table to
answer the question.
If one person is
selected to win a
door prize, what is
the probability he/she
is not Danish?
a.
37
 0.153
242
c.
205
 0.847
242
Nationality
English
Norwegian
Danish
German
French
Italian
Frequency
42
73
37
26
13
51
b.
73
 0.302
242
d.
169
 0.698
242
Slide 6 - 23
In 2007, Ben Sheets’ record as a pitcher for the
Milwaukee Brewers was 12 wins and 5 losses. In
those 17 games he gave up the following number
of hits: 2, 4, 8, 6, 4, 5, 4, 11, 7, 8, 6, 5, 6, 8, 6, 6, 6.
Given that Ben Sheets wins or loses a game,
estimate the probability that he gives up fewer
than 6 hits.
a.
6
 0.353
17
11
 0.647
17
b.
c.
6
 0.5
12
d. can’t determine
Slide 6 - 24
In 2007, Ben Sheets’ record as a pitcher for the
Milwaukee Brewers was 12 wins and 5 losses. In
those 17 games he gave up the following number
of hits: 2, 4, 8, 6, 4, 5, 4, 11, 7, 8, 6, 5, 6, 8, 6, 6, 6.
Given that Ben Sheets wins or loses a game,
estimate the probability that he gives up fewer
than 6 hits.
a.
6
 0.353
17
11
 0.647
17
b.
c.
6
 0.5
12
d. can’t determine
Slide 6 - 25
A loaded die has the
given probabilities. If
you roll this die 630
times, how many
times should you
expect to see the
number 3?
Number
1
2
3
4
5
6
Probability
1/21
2/21
3/21
4/21
5/21
6/21
a.
1
 630  30
21
2
 630  60
21
b.
c.
3
 630  90
21
4
d.
 630  120
21
Slide 6 - 26
A loaded die has the
given probabilities. If
you roll this die 630
times, how many
times should you
expect to see the
number 3?
Number
1
2
3
4
5
6
Probability
1/21
2/21
3/21
4/21
5/21
6/21
a.
1
 630  30
21
2
 630  60
21
b.
c.
3
 630  90
21
4
d.
 630  120
21
Slide 6 - 27
Suppose you pay $2
to roll the die and
win $6 if it comes up
a 1 or 6, but nothing
otherwise. What is
your expected value?
Number
1
2
3
4
5
6
Probability
1/21
2/21
3/21
4/21
5/21
6/21
a. $0
b. $0.67
c. $2
d. $6
Slide 6 - 28
Suppose you pay $2
to roll the die and
win $6 if it comes up
a 1 or 6, but nothing
otherwise. What is
your expected value?
Number
1
2
3
4
5
6
Probability
1/21
2/21
3/21
4/21
5/21
6/21
a. $0
b. $0.67
c. $2
d. $6
Slide 6 - 29
In 2003, the U. S. death rate was 1.2 per 100,000
people due to motorcycle accidents. Motorcycles
in the U. S. were involved in fatal crashes are the
rate of 35.0 per 100 million miles drive. If the
population of the U. S. is 300,000,000, what is the
expected number of deaths due to motorcycle
accidents?
a. 1200
b. 2400
c. 3500
d. 3600
Slide 6 - 30
In 2003, the U. S. death rate was 1.2 per 100,000
people due to motorcycle accidents. Motorcycles
in the U. S. were involved in fatal crashes are the
rate of 35.0 per 100 million miles drive. If the
population of the U. S. is 300,000,000, what is the
expected number of deaths due to motorcycle
accidents?
a. 1200
b. 2400
c. 3500
d. 3600
Slide 6 - 31
Use the table to find what age a female of age 60
may expect to live on the average.
Exact age
50
60
70
Female
P(Death within Number of
one year)
Living
0.003240
95,378
0.007740
90,847
0.008938
80,583
a. 91.91
b. 83.21
c. 75.45
d. 85.45
Life
Expectancy
31.91
23.21
15.45
Slide 6 - 32
Use the table to find what age a female of age 60
may expect to live on the average.
Exact age
50
60
70
Female
P(Death within Number of
one year)
Living
0.003240
95,378
0.007740
90,847
0.008938
80,583
a. 91.91
b. 83.21
c. 75.45
d. 85.45
Life
Expectancy
31.91
23.21
15.45
Slide 6 - 33
Use the table to find how many 60-year old
females on average will be living at age 61.
Exact age
50
60
70
Female
P(Death within Number of
one year)
Living
0.003240
95,378
0.007740
90,847
0.008938
80,583
Life
Expectancy
31.91
23.21
15.45
a. 90,847
b. 80,583
c. 90,144
d. 90,062
Slide 6 - 34
Use the table to find how many 60-year old
females on average will be living at age 61.
Exact age
50
60
70
Female
P(Death within Number of
one year)
Living
0.003240
95,378
0.007740
90,847
0.008938
80,583
Life
Expectancy
31.91
23.21
15.45
a. 90,847
b. 80,583
c. 90,144
d. 90,062
Slide 6 - 35