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Slide 10 - 1Copyright © 2009 Pearson Education, Inc.
Active Learning Lecture SlidesFor use with Classroom Response Systems
© 2009 Pearson Education, Inc.All rights reserved.
Chapter 10Counting
and Probability
Slide 10 - 2Copyright © 2009 Pearson Education, Inc.
Write down all the subsets of {x, y, z}.
a.
b.
c.
d.
x , y , z , x, y , x, z , y, z , x, y, z ,
x , y , z , x, y , x, z , y, z , x, y, z
x , y , z , x, y , x, z , y, z ,
x , y , z , x, y , x, z , y, z ,
x, x , y, y , z, z , x, y, z ,
Slide 10 - 3Copyright © 2009 Pearson Education, Inc.
Write down all the subsets of {x, y, z}.
a.
b.
c.
d.
x , y , z , x, y , x, z , y, z , x, y, z ,
x , y , z , x, y , x, z , y, z , x, y, z
x , y , z , x, y , x, z , y, z ,
x , y , z , x, y , x, z , y, z ,
x, x , y, y , z, z , x, y, z ,
Slide 10 - 4Copyright © 2009 Pearson Education, Inc.
a. 10
b. 12
c. 14
d. 9
If 12, 3, and 21,
find .
n B n A B n A B
n A
Slide 10 - 5Copyright © 2009 Pearson Education, Inc.
a. 10
b. 12
c. 14
d. 9
If 12, 3, and 21,
find .
n B n A B n A B
n A
Slide 10 - 6Copyright © 2009 Pearson Education, Inc.
a. 44
b. 38
c. 50
d. 45
Use the Venn Diagram to find how many are not in C.
Slide 10 - 7Copyright © 2009 Pearson Education, Inc.
a. 44
b. 38
c. 50
d. 45
Use the Venn Diagram to find how many are not in C.
Slide 10 - 8Copyright © 2009 Pearson Education, Inc.
a. 25 b. 5
c. 15 d. 35
In a survey of 50 households, 25 responded that they have an HDTV television , 35 responded that they had a multimedia personal computer, and 15 responded they had both. How many households had neither an HDTV television nor a multimedia personal computer?
Slide 10 - 9Copyright © 2009 Pearson Education, Inc.
a. 25 b. 5
c. 15 d. 35
In a survey of 50 households, 25 responded that they have an HDTV television , 35 responded that they had a multimedia personal computer, and 15 responded they had both. How many households had neither an HDTV television nor a multimedia personal computer?
Slide 10 - 10Copyright © 2009 Pearson Education, Inc.
a. 150
b. 18
c. 50
d. 300
A restaurant offers a choice of 5 salads, 10 main courses, and 3 desserts. How many possible 3-course meals are there?
Slide 10 - 11Copyright © 2009 Pearson Education, Inc.
a. 150
b. 18
c. 50
d. 300
A restaurant offers a choice of 5 salads, 10 main courses, and 3 desserts. How many possible 3-course meals are there?
Slide 10 - 12Copyright © 2009 Pearson Education, Inc.
a. 6
b. 676,000
c. 36
d. 260
How many different license plates can be made using 2 letters followed by 3 digits selected from the digits 0 through 9, if letters and digits may be repeated?
Slide 10 - 13Copyright © 2009 Pearson Education, Inc.
a. 6
b. 676,000
c. 36
d. 260
How many different license plates can be made using 2 letters followed by 3 digits selected from the digits 0 through 9, if letters and digits may be repeated?
Slide 10 - 14Copyright © 2009 Pearson Education, Inc.
a. 12
b. 4
c. 24
d. 6
4 different books are to be arranged on a shelf. How many different arrangements are possible?
Slide 10 - 15Copyright © 2009 Pearson Education, Inc.
a. 12
b. 4
c. 24
d. 6
4 different books are to be arranged on a shelf. How many different arrangements are possible?
Slide 10 - 16Copyright © 2009 Pearson Education, Inc.
a. 17,576,000
b. 3095.2381
c. 12,654,720
d. 15,600,000
How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?
Slide 10 - 17Copyright © 2009 Pearson Education, Inc.
a. 17,576,000
b. 3095.2381
c. 12,654,720
d. 15,600,000
How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?
Slide 10 - 18Copyright © 2009 Pearson Education, Inc.
a. 2520
b. 5040
c. 151,200
d. 210
From 10 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?
Slide 10 - 19Copyright © 2009 Pearson Education, Inc.
a. 2520
b. 5040
c. 151,200
d. 210
From 10 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?
Slide 10 - 20Copyright © 2009 Pearson Education, Inc.
a. 36,288,000
b. 646,646
c. 42,000
d. 165
How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 5 forwards, 7 midfield players, and 10 defensive players?
Slide 10 - 21Copyright © 2009 Pearson Education, Inc.
a. 36,288,000
b. 646,646
c. 42,000
d. 165
How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 5 forwards, 7 midfield players, and 10 defensive players?
Slide 10 - 22Copyright © 2009 Pearson Education, Inc.
a. 3,628,800
b. 453,600
c. 907,200
d. 45,360
How many different 10-letter words (real or imaginary) can be formed from the letters in the word PHILOSOPHY?
Slide 10 - 23Copyright © 2009 Pearson Education, Inc.
a. 3,628,800
b. 453,600
c. 907,200
d. 45,360
How many different 10-letter words (real or imaginary) can be formed from the letters in the word PHILOSOPHY?
Slide 10 - 24Copyright © 2009 Pearson Education, Inc.
a. 140
b. 9
c. 15
d. 35
How many different vertical arrangements are there of 7 flags if 3 are white, 3 are blue, and 1 is red?
Slide 10 - 25Copyright © 2009 Pearson Education, Inc.
a. 140
b. 9
c. 15
d. 35
How many different vertical arrangements are there of 7 flags if 3 are white, 3 are blue, and 1 is red?
Slide 10 - 26Copyright © 2009 Pearson Education, Inc.
a. Yes
b. No
Determine whether the following is a probability model.
Outcome Probability
Red 0.24
Blue 0.26
Green 0.31
White 0.19
Slide 10 - 27Copyright © 2009 Pearson Education, Inc.
a. Yes
b. No
Determine whether the following is a probability model.
Outcome Probability
Red 0.24
Blue 0.26
Green 0.31
White 0.19
Slide 10 - 28Copyright © 2009 Pearson Education, Inc.
a. Yes
b. No
Determine whether the following is a probability model.
Outcome Probability
Red 0.16
Blue 0.23
Green 0.35
White 0.50
Slide 10 - 29Copyright © 2009 Pearson Education, Inc.
a. Yes
b. No
Determine whether the following is a probability model.
Outcome Probability
Red 0.16
Blue 0.23
Green 0.35
White 0.50
Slide 10 - 30Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
A bag contains 6 red marbles, 7 blue marbles, and 8 green marbles. If one marble is selected at random, determine the probability that it is blue.
1
3
2
7
8
21
7
13
Slide 10 - 31Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
A bag contains 6 red marbles, 7 blue marbles, and 8 green marbles. If one marble is selected at random, determine the probability that it is blue.
1
3
2
7
8
21
7
13
Slide 10 - 32Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 5?
1
9
5
6
8
94
Slide 10 - 33Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 5?
1
9
5
6
8
94
Slide 10 - 34Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
What is the probability that the arrow will land on an odd number, assuming all sectors have equal area?
3
5
2
5
1 0
Slide 10 - 35Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
What is the probability that the arrow will land on an odd number, assuming all sectors have equal area?
3
5
2
5
1 0
Slide 10 - 36Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
Find the probability of getting 2 tails when 3 fair coins are tossed.
1
4
3
8
2
3
1
2
Slide 10 - 37Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
Find the probability of getting 2 tails when 3 fair coins are tossed.
1
4
3
8
2
3
1
2
Slide 10 - 38Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
Find the probability of having 4 girls in a 4-child family.
1
4
1
8
1
16
1
32
Slide 10 - 39Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
Find the probability of having 4 girls in a 4-child family.
1
4
1
8
1
16
1
32
Slide 10 - 40Copyright © 2009 Pearson Education, Inc.
a. 0.75 b. 0.87
c. 0.93 d. 0.81
Given that P(A) = 0.62, P(B) = 0.25, and
P A B 0.06, find P A B .
Slide 10 - 41Copyright © 2009 Pearson Education, Inc.
a. 0.75 b. 0.87
c. 0.93 d. 0.81
Given that P(A) = 0.62, P(B) = 0.25, and
P A B 0.06, find P A B .
Slide 10 - 42Copyright © 2009 Pearson Education, Inc.
a. 0.6445 b. 0.1155
c. 0 d. 0.76
Given that P(A) = 0.21, P(B) = 0.55, findP A B if A and B are mutually exclusive.
Slide 10 - 43Copyright © 2009 Pearson Education, Inc.
a. 0.6445 b. 0.1155
c. 0 d. 0.76
Given that P(A) = 0.21, P(B) = 0.55, findP A B if A and B are mutually exclusive.
Slide 10 - 44Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?
7
9
2
3
1
312
Slide 10 - 45Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?
7
9
2
3
1
312
Slide 10 - 46Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
The psychology lab at a college is staffed by 6 male doctoral students, 12 female doctoral students, 14 male undergraduates and 7 female undergraduates. If a person is selected at random from the group, find the probability that the selected person is an undergraduate or a female.
2
3
11
13
7
13
19
39
Slide 10 - 47Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
The psychology lab at a college is staffed by 6 male doctoral students, 12 female doctoral students, 14 male undergraduates and 7 female undergraduates. If a person is selected at random from the group, find the probability that the selected person is an undergraduate or a female.
2
3
11
13
7
13
19
39
Slide 10 - 48Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
A bag contains 6 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?
7
11
11
7
4
117
Slide 10 - 49Copyright © 2009 Pearson Education, Inc.
a. b.
c. d.
A bag contains 6 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?
7
11
11
7
4
117
Slide 10 - 50Copyright © 2009 Pearson Education, Inc.
a. 0.956 b. 0.046
c. 0.954 d. 0.044
What is the probability that at least 2 people have the same birth month in a group of 8 people?
Slide 10 - 51Copyright © 2009 Pearson Education, Inc.
a. 0.956 b. 0.046
c. 0.954 d. 0.044
What is the probability that at least 2 people have the same birth month in a group of 8 people?
