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Name Class Date Extra Practice
Chapter 11
Lessons 11-1
Evaluate each expression.
1. 6! 720
2. 3!4! 144
7!
3. 4! 210
6!2! 1
4. 8! 28
5. 8P5 6720
6. 4C1 4
7. 6C2 15
8. 6P2 30
9. 7C3 35
10. 7P3 210
7C5
12. C 2.1
5 2
11. 2(7C5) 42
For each situation, determine whether to use a permutation or a combination.
Then solve the problem.
13. How many different orders can you choose to read six of the nine books on
your summer reading list? permutation; 60,480 orders
14. How many ways are there to choose five shirts out of seven to take to camp?
combination; 21 ways
15. How many ways can you choose two out of four kinds of flowers for a bouquet?
combination; 6 ways
16. You must answer exactly 12 out of 15 questions on a test. How many different
ways can you select the questions to answer? combination; 455 ways
17. A lab assigns a unique three-digit identification to each subject in an
experiment. No digit can be repeated in an identification. What is the greatest
number of subjects that can be used in the experiment? permutation; 720 orders
18. To mark its eighth anniversary, Pizzeria Otto has a special coupon that offers
the same price on a pizza with any combination of the 8 original toppings.
Each pizza must have at least one topping. How many different kinds of pizza
can be ordered with the coupon? combination; 255 kinds of pizza
Lessons 11-2
19. A class rolled a number cube 40 times and recorded an even number 23 times.
What is the experimental probability of rolling an even number? odd number?
23 17
40 ; 40
Evaluate each expression.
1
20. P(club) 4
1
21. P(4 of hearts) 52
1
22. P(ace) 13
23. On a multiple-choice test, each item has 5 choices, but only one choice is
correct. How can you simulate guessing each answer on a 20-question test?
Answers may vary. Sample: You can pick at random from five numbers, specifying that one
of them will be the “correct” answer. This can be repeated for each of the 20 questions.
24. To score a point in a certain party game, a thrown bean bag must land in a circle with a
2-foot diameter. If the playing field is a 10-foot by 12-foot rectangle, what is the probability
that a bean bag that lands randomly in the playing field will score a point? 0.026
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Name Class Date Extra Practice (continued)
Chapter 11
Lessons 11-3
Classify each pair of events as dependent or independent.
25. A number cube is rolled; the number cube is rolled again. independent
26. A marble is chosen out of a bag; another remaining marble is chosen out
of the bag. dependent
Q and R are independent events. Find P(Q and R).
1
1 1
27. P(Q) 5 4 , P(R) 5 8 36
7
2
28. P(Q) 5 7 , P(R) 5 9 29
29. P(Q) 5 0.4, P(R) 5 0.15
0.06
Two fair number cubes are tossed. State whether the events are mutually
exclusive. Explain your reasoning.
30. The sum is 10; the numbers are equal. not mutually exclusive; 5 1 5 5 10
31. The sum is greater than 9; one of the numbers is 2.
Mutually exclusive; if one number cube is 2, then the sum of both cannot be
greater than 8.
S and T are mutually exclusive events. Find P(S or T).
7
1
33. P(S) 5 15 , P(T) 5 5 2
3
1
2
32. P(S) 5 6 , P(T) 5 3 56
34. P(S) 5 18%, P(T) 5 44%
62%
A fair number cube is tossed. Find each probability.
1
5
35. P(6 or even) 2
36. P(even or more than 1) 6
Lessons 11-4
Characteristics of Comp Counselors
Use the table to find each probability.
38. P(counselor a junior)
39
80
39. P(counselor female) 37
80
37. P(even or prime) 1
25
Grade Level
Male
Female
Junior
18
21
Senior
25
16
40. P(counselor a senior and male) 80
21
41. P(counselor a junior | counselor female) 37
25
42. P(counselor male | counselor a senior) 41
3
43. The probability that Luis wins the election for class president is 5 .
2
The probability that Mac wins the election for class treasurer is 3 .
1
The probability that both will win the office they are running for is 2 .
What is the probability that Luis wins given that Mac wins?
3
4
44. You toss two number cubes. The sum of the numbers is greater than 5. What is
4
2
or 13
the probability that you tossed the same number on each cube? 26
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Name Class Date Extra Practice (continued)
Chapter 11
Lessons 11-5
Determine whether the strategies described result in a fair decision. Explain.
45. The academic team has 12 players. The coach wants to pick 2 of the players as
captains of the team. The coach writes each player’s name on a piece of paper,
places the names in a bag, and chooses 2 at random.
Fair; each student has an equal chance of being picked.
46. Mrs. Jackson is a history teacher. To choose two students at random, she
decides to choose the tallest and shortest students in the class.
Not fair; each student does not have an equal chance of being picked.
Lessons 11-6
Find the mean, median, and mode of each set of values.
47. 3 2 6 4 5 3 4 2 7 5 3 4; 4; 3
48. 16 62 24 13 21 35 24 17 20 25.5; 21; 24
49. 125 135 126 138 137 135 121 131; 135; 135 50. 6.1 9.5 3.8 4.6 6.1 2.3 3.7 2.1 4.8; 4.2; 6.1
51. All the scores on an Advanced Algebra final exam are shown below.
59 62 63 63 72 74 74 78 79 81
83 84 84 84 89 90 92 94 96 98
a. Find the mean, median, and mode for the data. 79.95; 82; 84
b. What percentile is the student who scored 89? 70th percentile
c. Draw a box-and-whisker plot for the data.
60
70
80
90
100
d. Identify any outliers in the data. Explain your choice.
Answers may vary. Sample: None; all the scores are reasonably close to each other.
Lessons 11-7
Find the mean, variance, and standard deviation for each data set.
52. 6 8 5 2 7 3 5 6 7 5.44; 3.35; 1.83
53. 25 29 21 19 30 26 28 25.43; 14.52; 3.81
54. 12 9 10 11 13 9 20 12; 12.57; 3.55
55. 100 98 101 100 102 97 100
99.71; 2.49; 1.58
Lessons 11-8
56. The school principal wants to find out how many students support starting a lacrosse
team. The principal interviews students at random as they watch a soccer game. What
sampling method was used? Identify any bias in the method.
Convenience sample; answers may vary. Sample: People interviewed at a sporting
event may be more likely to support starting a new sports team.
57. The mayor of your town is running for re-election. What sampling method could you
use to find the percent of registered voters in your town who plan to re-elect the mayor?
What is an example of a survey question that is likely to yield unbiased information?
Answers may vary. Sample: You can contact voters, randomly selected from a list of
all registered voters in your town, and ask, “If the election were held today, would
you vote to re-elect the mayor?”
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Name Class Date Extra Practice (continued)
Chapter 11
Lessons 11-9
Find the probability of x successes in n trials for the given probability of success
p on each trial.
58. x 5 2, n 5 6, p 5 0.7
0.0595 < 6%
2
59. x 5 3, n 5 8, p 5 5 0.2787 < 28%
60. x 5 9, n 5 10, p 5 0.3
0.0001 < 0.01%
1
61. x 5 7, n 5 9, p 5 5 0.0003 < 0.03%
62. x 5 4, n 5 12, p 5 0.8
0.00052 < 0.05%
63. x 5 9, n 5 11, p 5 0.9
0.0710 < 7%
Use the binomial expansion of (p 1 q)n to calculate each binomial distribution.
64. n 5 5, p 5 0.2
P(k
P(k
P(k
P(k
P(k
P(k
65. n 5 6, p 5 0.4
5 0) 5 0.32768
5 1) 5 0.4096
5 2) 5 0.2048
5 3) 5 0.0512
5 4) 5 0.0064
5 5) 5 0.00032
P(k
P(k
P(k
P(k
P(k
P(k
P(k
5 0)
5 1)
5 2)
5 3)
5 4)
5 5)
5 6)
66. p 5 5, p 5 0.7
5 0.0467
5 0.1866
5 0.3110
5 0.2765
5 0.1382
5 0.0369
5 0.0041
P(k
P(k
P(k
P(k
P(k
P(k
5 0)
5 1)
5 2)
5 3)
5 4)
5 5)
5 0.00243
5 0.02835
5 0.1323
5 0.3087
5 0.36015
5 0.16807
67. Jean is visiting her grandparents in Houston for five days. She wants to arrange
a lunch with friends. If she picks a day at random, there is a 20% chance that
all of her friends will be available to meet for lunch. What is the probability
that all her friends are available to meet for lunch on three different days?
about 5.12%
Lessons 11-10
Sketch a normal curve for each distribution. Label the x-axis values at one, two,
and three standard deviations from the mean.
68. mean 5 30, standard deviation 5 4
69. mean 5 45, standard deviation 5 11
18 22 26 30 34 38 42
−3σ −2σ −1σ x +1σ +2σ +3σ
12
23
34
−3σ −2σ −1σ
45
x
56
67
78
+1σ +2σ +3σ
70. The mean score on a quiz is 82 out of 100 possible points and the standard
deviation is 4. Estimate the percent of scores that were 90 or higher. 2.5%
71. A psychology professor gives a 100-item true/false test in a large college class.
The mean score is 75.2, and the standard deviation is 8.1. The scores follow a
normal distribution. What is the minimum score that is in the 99th percentile? 94
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