Math for liberal arts homework

MGF1106 Test 4 Review

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. You are not required to show work, however, partial credit may be given if work is provided.

Solve the problem by applying the Fundamental Counting Principle with two groups of items. 1) A restaurant offers a choice of 4 salads, 10 main courses, and 4 desserts. How many possible

3-course meals are there? A) 160 B) 18 C) 320 D) 40

1)

2) An apartment complex offers apartments with four different options, designated by A through D.

A = number of bedrooms (one through four) B = number of bathrooms (one through three) C = floor (first through fifth) D = outdoor additions (balcony or no balcony)

How many apartment options are available? A) 14 B) 120 C) 16 D) 240

2)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

3) Jamie is joining a music club. As part of her 4-CD introductory package, she can choose from 12 rock selections, 10 alternative selections, 7 country selections and 5 classical selections. If Jamie chooses one selection from each category, how many ways can she choose her introductory package?

3)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. You are not required to show work, however, partial credit may be given if work is provided.

Solve the problem. 4) In how many distinct ways can the letters in PHILOSOPHY be arranged?

A) 3,628,800 B) 45,360 C) 453,600 D) 907,200 4)

Use the formula for nPr to solve. 5) How many arrangements can be made using 3 letters of the word HYPERBOLAS if no letter is

to be used more than once? A) 1,209,600 B) 720 C) 120 D) 604,800

5)

Use the Fundamental Counting Principle to solve the problem. 6) You want to arrange 7 of your favorite CD's along a shelf. How many different ways can you

arrange the CD's assuming that the order of the CD's makes a difference to you? A) 49 B) 720 C) 42 D) 5040

6)

Use the formula for nCr to evaluate the expression.

7) 6C4 A) 15 B) 4 C) 180 D) 30

7)

1

Evaluate the expression.

8) 1 - 7 P5

8P4

A) 1 4

B) 3 4

C) 3 2

D) 1 2

8)

9) 6 P2 2!

- 6C2

A) 2 B) 1 C) 0 D) 1 2

9)

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms.

10) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 7.

A) 8 B) 4 13

C) 13 2

D) 2 13

10)

11) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 3.

A) 0 B) 1 6

C) 1 2

D) 3

11)

Solve the problem. 12) Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive

randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last.

A) 720; 15; 1 48

B) 120; 6; 1 20

C) 120; 10; 1 12

D) 720; 24; 1 30

12)

13) If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3 jacks and 3 aces.

A) 1 1017926

B) 2 2544815

C) 2 13

D) 3 26

13)

14) A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many ways can 4 people be selected from this group of 11? In how many ways can 4 men be selected from the 6 men? Find the probability that the selected group will consist of all men.

A) 7920; 360; 1 22

B) 330; 15; 1 1814400

C) 330; 15; 1 22

D) 330; 15; 1 15840

14)

2

Solve the problem that involves probabilities with events that are not mutually exclusive. 15) In a class of 50 students, 21 are Democrats, 9 are business majors, and 7 of the business majors

are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major.

A) 3 5

B) 1 25

C) 37 50

D) 23 50

15)

Solve the problem involving probabilities with independent events. 16) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is

shuffled, and you draw again. Find the probability of getting a picture card the first time and a club the second time.

A) 1 4

B) 1 13

C) 3 13

D) 3 52

16)

Solve the problem. 17) The table shows the number of minority officers in the U.S. military.

Army Navy Marines Air Force African Americans 9162 3524 1341 4282 Hispanic Americans 2105 2732 914 1518 Other Minorities 4075 2653 599 3823

Assume that one person will be randomly selected from the group described in the table. Find the probability of selecting an officer who is in the Navy, given that the officer is African American.

A) 8909 18,309

B) 3524 8909

C) 3542 14785

D) 3524 18,309

17)

Solve the problem involving probabilities with independent events. 18) The chart shows a certain city's population by age. Assume that the selections are independent

events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.

City X's Population by Age 0-24 years old 33% 25-44 years old 22% 45-64 years old 21% 65 or older 24%

A) 0.000067 B) 0.000244 C) 0.000129 D) 0.000014

18)

3

Answer Key Testname: MGF1106_TEST_4_REVIEW

1) A 2) B 3) 4200 4) C 5) B 6) D 7) A 8) C 9) C

10) D 11) B 12) D 13) B 14) C 15) D 16) D 17) D 18) D

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