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A P P E N D I X C . 5

Probability Distributions

The following warm-up exercises involve skills that were covered in earlier sections. You will use

Skills Review C.5

these skills in the exercise set for this section. For additional help, review Section C.1.

In Exercises 1–3, determine the sample space for the experiment.

1. Two coins are removed at random from a purse that contains pennies, nickels, dimes, and quarters.

2. Two four-sided dice are tossed and the sum of the points is recorded.

3. One six-sided die and one four-sided die are tossed and the sum of the points is recorded.

In Exercises 4– 6, find the indicated probability. Use the results of Exercises 1–3.

4. Two coins are removed at random from a purse that contains pennies, nickels, dimes, and quarters. What is the

probability that both coins are pennies?

5. Two four-sided dice are tossed and the sum of the points is recorded. What is the probability that the sum of the

points is 6?

6. One six-sided die and one four-sided die are tossed and the sum of the points is recorded. What is the probability

that the sum of the points is 6?

Exercises C.5

See for worked-out solutions to odd-numbered exercises.

Coin Toss

In Exercises 7–10, use the following data

1.

A coin is tossed twice. A random variable

assigns the number 0, 1, or 2 to each possible outcome,

26

5

19

34

17

33

19

16

32

12

depending on the number of tails that turn up. Find the

23

36

28

32

4

35

10

39

2

20

frequencies of 0, 1, and 2.

37

18

18

23

8

6

14

12

16

21

2.

Two Coins

You have a mixture of pennies, nickels,

35

9

39

15

21

13

20

32

26

25

dimes, and quarters in your pocket. You remove one coin

7. Construct a frequency distribution using intervals of width

from your pocket at random, then another. A random

5, starting with the interval

0 < x ≤ 5.

variable assigns the number 0, 1, or 2 to each possible

8. Construct a frequency distribution using intervals of width

outcome, depending on the number of pennies that you

8, starting with the interval

0 < x ≤ 8.

remove. Find the frequencies of 0, 1, and 2.

9. Construct a frequency distribution using intervals of width

Dice

3.

Two four-sided dice are tossed. Let the random

7, starting with the interval

1 < x ≤ 8.

variable be the sum of the points on the two dice. Find the

x

frequency of each possible value of

x.

10. Construct a frequency distribution using intervals of width

9, starting with the interval

1 < x ≤ 10.

Dice

4.

One six-sided die and one four-sided die are tossed.

Let the random variable

x

be the sum of the points on the

Numbers of Employees

11.

Twenty medium-sized com-

two dice. Find the frequency of each possible value of

x.

panies (between 50 and 100 employees) are located in the

5.

Exam

Two students answer a true-false question on an

same city. The numbers of employees of the companies are

examination. A random variable assigns the number 0, 1, or

as follows.

2 to each outcome, depending on the number of answers of

54 94 78 100 87 67 100 97 75 92

true among the two students. Find the frequencies of 0, 1,

73 70 82

79 91 80

78 72 60 86

and 2.

(a) Construct a frequency distribution using the following

Exam

6.

Five students answer a true-false question on an

ranges: 50–59, 60–69, 70–79, 80–89, 90–100.

examination. A random variable assigns the number 0, 1, 2,

3, 4, or 5 to each outcome, depending on the number of

(b) Construct a histogram for the frequency distribution.

answers of true among the five students. Find the frequen-

cies of 0, 1, 2, 3, 4, and 5.

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