1. Counting and Probability
Active Learning Lecture Slides
For use with Classroom Response Systems
© 2009 Pearson Education, Inc.
All rights reserved.
Chapter 10
Counting and Probability

2. Write down all the subsets of {x, y, z}.c. d.

3. Write down all the subsets of {x, y, z}.c. d.

4. a. 10
b. 12
c. 14
d. 9

5. a. 10
b. 12
c. 14
d. 9

6. Use the Venn Diagram to find how many are not in C.
b. 38
c. 50
d. 45

7. Use the Venn Diagram to find how many are not in C.
b. 38
c. 50
d. 45

8. 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?
a. 25 b. 5
c. 15 d. 35

9. 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?
a. 25 b. 5
c. 15 d. 35

10. A restaurant offers a choice of 5 salads, 10 main courses, and 3 desserts. How many possible 3-course meals are there?
a. 150
b. 18
c. 50
d. 300

11. A restaurant offers a choice of 5 salads, 10 main courses, and 3 desserts. How many possible 3-course meals are there?
a. 150
b. 18
c. 50
d. 300

12. 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?
a. 6
b. 676,000
c. 36
d. 260

13. 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?
a. 6
b. 676,000
c. 36
d. 260

14. 4 different books are to be arranged on a shelf
4 different books are to be arranged on a shelf. How many different arrangements are possible?
a. 12
b. 4
c. 24
d. 6

15. 4 different books are to be arranged on a shelf
4 different books are to be arranged on a shelf. How many different arrangements are possible?
a. 12
b. 4
c. 24
d. 6

16. 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?
a. 17,576,000 b
c. 12,654,720
d. 15,600,000

17. 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?
a. 17,576,000 b
c. 12,654,720
d. 15,600,000

18. 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?
a. 2520
b. 5040
c. 151,200
d. 210

19. 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?
a. 2520
b. 5040
c. 151,200
d. 210

20. 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?
a. 36,288,000
b. 646,646
c. 42,000
d. 165

21. 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?
a. 36,288,000
b. 646,646
c. 42,000
d. 165

22. How many different 10-letter words (real or imaginary) can be formed from the letters in the word PHILOSOPHY?
a. 3,628,800
b. 453,600
c. 907,200
d. 45,360

23. How many different 10-letter words (real or imaginary) can be formed from the letters in the word PHILOSOPHY?
a. 3,628,800
b. 453,600
c. 907,200
d. 45,360

24. How many different vertical arrangements are there of 7 flags if 3 are white, 3 are blue, and 1 is red?
a. 140
b. 9
c. 15
d. 35

25. How many different vertical arrangements are there of 7 flags if 3 are white, 3 are blue, and 1 is red?
a. 140
b. 9
c. 15
d. 35

26. Determine whether the following is a probability model.
Outcome
Probability
Red
0.24
Blue
0.26
Green
0.31
White
0.19
a. Yes
b. No

27. Determine whether the following is a probability model.
Outcome
Probability
Red
0.24
Blue
0.26
Green
0.31
White
0.19
a. Yes
b. No

28. Determine whether the following is a probability model.
Outcome
Probability
Red
0.16
Blue
0.23
Green
0.35
White
0.50
a. Yes
b. No

29. Determine whether the following is a probability model.
Outcome
Probability
Red
0.16
Blue
0.23
Green
0.35
White
0.50
a. Yes
b. No

30. A bag contains 6 red marbles, 7 blue marbles, and 8 green marbles
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.
a. b.
c. d.

31. A bag contains 6 red marbles, 7 blue marbles, and 8 green marbles
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.
a. b.
c. d.

32. Two 6-sided dice are rolled
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 5?
a. b.
c. d.

33. Two 6-sided dice are rolled
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 5?
a. b.
c. d.

34. What is the probability that the arrow will land on an odd number, assuming all sectors have equal area?
a. b.
c. d.

35. What is the probability that the arrow will land on an odd number, assuming all sectors have equal area?
a. b.
c. d.

36. Find the probability of getting 2 tails when 3 fair coins are tossed.
c. d.

37. Find the probability of getting 2 tails when 3 fair coins are tossed.
c. d.

38. Find the probability of having 4 girls in a 4-child family.
c. d.

39. Find the probability of having 4 girls in a 4-child family.
c. d.

40. Given that P(A) = 0.62, P(B) = 0.25, and
a b. 0.87
c d. 0.81

41. Given that P(A) = 0.62, P(B) = 0.25, and
a b. 0.87
c d. 0.81

42. Given that P(A) = 0.21, P(B) = 0.55, find
if A and B are mutually exclusive.
a b
c. 0 d. 0.76

43. Given that P(A) = 0.21, P(B) = 0.55, find
if A and B are mutually exclusive.
a b
c. 0 d. 0.76

44. A spinner has regions numbered 1 through 15
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?
a. b.
c. d.

45. A spinner has regions numbered 1 through 15
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?
a. b.
c. d.

46. 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.
a. b.
c. d.

47. 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.
a. b.
c. d.

48. A bag contains 6 red marbles, 4 blue marbles, and 1 green marble
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?
a. b.
c. d.

49. A bag contains 6 red marbles, 4 blue marbles, and 1 green marble
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?
a. b.
c. d.

50. What is the probability that at least 2 people have the same birth month in a group of 8 people?
c d

51. What is the probability that at least 2 people have the same birth month in a group of 8 people?
c d