3.1 Sample Spaces and Events

Chapter 3 – An Introduction to Probability Answer Key

CK-12 Advanced Probability and Statistics

Concepts 1

3.1 Sample Spaces and Events

Answers

1. a)

Events 1H 1T 2H 2T 3H 3T 4H 4T 5H 5T 6H 6T

Probabilit

y

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

b) P (2H) = 1/12

2. a) Same as 1a

b) Same as 1b

3. a)


Probabilit

y

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

b) P (even #) = 6/12 or ½

4. a)


Probabilit

y

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

1/1

2

b) P(T) = 6/12 or ½

5. P (A) = 4/9



Concepts 2

6. P (B) = 3/9 or 1/3



Concepts 3

7.a)

Events B1 B2 R1 R2 R3

Probability 1/5 1/5 1/5 1/5 1/5

b) P (2 blue) = 2 1 1

5 4 10

8. P (1 red and 1 blue) = 3 2 3

5 4 10

9. P (2 red) =

3 2 3

5 4 10

10. P(neither marble is blue or red) = 0

11. a) S={A, B, C, D}

b) S = {HH, HT, TH, TT}

c) S = {ABCD, ABDC,ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA,

CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB DBCA, DBAC, DCAB, DCBA}

12. a)

b)

TH

T

H

Coin B

Coin A

654321

T

H

Coin

Die



Concepts 4

c)

13. a)

1 H

T

2 H

T

3 H

T

4 H

T

5 H

T

6 H

T

A

B

654321

D

C

Spinner

Die



Concepts 5

b)

H T

H

T

H H

T

T

T H

T

H H

T

c)

P P

B

W

B

P

B

W

W

P

B

W

14. a) Yes

b) Yes

c) Yes

d) No, probability values are from 0 to 1.

e) No, probability values are from 0 to 1.



Concepts 6

15. a) There is a probability that 1

30 customers will return the appliance with two weeks of

purchase.

b) There is a probability that 3.33% chance that customers will return the appliance with two

weeks of purchase.

c) There is a probability of 0.033 that customers will return the appliance with two weeks of

purchase.

16. a) S={HHHH, HHHT, HHTH, HHTT, HTHH, HTTH, HTHT, HTTT, HTTH, THHH,THHT, THTH,

THTT, TTHH, TTHT, TTTH, TTTT}

b) S = [0, )

c) S = (300, 800)

d) S = [0, n], where n is the number of computer components



Concepts 7

3.2 Operations with Sets

Answers

1. P(5) = 1/6

2. P(2 or 3 dots) = 1 1 2 1

6 6 6 3or

3. P(all odd dots) = 1 1 1 3 1

6 6 6 6 2or

4. 1/52

5. P(J, Q, K, or A) = 4 4 4 4 16 4

52 52 52 52 52 13or

6. P(black card) = 26 1

52 2or

7. Drawing a face card and drawing a 5 or smaller are disjointed events. Drawing a face card

means drawing a Jack, Queen, or King in any suit. Draw a 5 or smaller means drawing an

Ace, 2, 3, 4, or 5 in any suit. These two choices do not overlap.

8. P(red card or a spade) = 26 13 39 1

52 52 52 4or

9. P(32) = 1

38

10. P(even number) = 19 1

38 2or

11. P(first 12 numbers) = 12 6

38 19or

12. P(four consecutive numbers) = 36 2 1 1 72 1

38 37 36 35 1771560 24605or



Concepts 8

3.3 Complementary Rule for Probability

Answers

1. S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

2. S(A) = {HHH, HHT, HTH, HTT, THH, THT, TTH}

3. S(B) = {HHH, HTT, THT, TTH}

4. { , , , }A B HHH HTT THT TTH

A’={TTT}

{ , , , , , , }A B HHH HHT HTT HTH THH THT TTH

5. P(A)=7

8

P(B) =4 1

8 2or

( )P A B 7

8

P(A’) =1

8

( )P A B 4 1

8 2or

6. P (A’) =

4 2

10 5or

7. P (B’) =

2 1

10 5or

8. P A B 3

10

9. P A B

5 1

10 2or

10. P A B

7

10



Concepts 9

11.( )P A B 9

10

12.( ')P A B 1

10

13.[( ) ']P A B 1

10



Concepts 10

3.4 Conditional Probability

Answers

1. 3/4

2. 1/2

3. 1/2

4. 1

5. 1

6. 1/3

7 0

8. 1/6

9. 1/3

10. 5/6

11. same question as #10

12. ( ) 0.214P A B , ( ) 0.5P B A

13. a) 70

b) 31

c)

Seniors Non-senior

Liberal Arts 32 98 130

Science 31 39 70

63 137 200

d) 31.5%

e)

f) 31 32

100 31.5%200

35%

Liberal Arts

Science

Seniors 65%

Non-seniors

Non-seniors

Non-seniors

200 students

25%

75%

45%

55%



Concepts 11

14. 2

5

15. 1

3

16. a) ( )P A B

b) ( )P A B

c) ( ' ')P A B

d) ( ) ( )P A P A B

e) ( )

( )

P A B

P A

17. a) 3

10

b) 14

15

c) 13

28

18. 0.15

19. a) P(Female and Color-Blind) = 0.026

b) P(Male and Not color-blind) = 0.085

20. a) 5

72

b) 5

18

21. 0.025



Concepts 12

3.5 Additive and Multiplicative Rules for Probabilities

Answers

1. 1

12

2. 1

4

3. 5

12

4. 1

6

5. a) Yes because Event A does not depend on Event B.

b) No because both sets have 9 and 11.

6. 0.99

7. a) 1

8

b) 1

8

8. 1

16

9. a) 0.63

b) 0.03

c) 0.07

d) 0.27

10. a) 14

33

b) 8

33

c) 8

33

11. 0.193



Concepts 13

12. a) 0.25

b) 0.0625

c) 0.3125

d) 0.25

13. 3

7

14. a) S={CC, CM, MC, MM}

b) Yes

c) 1

4

15. a) No, there is nothing in common.

b) Yes, there is something in common (1)

S(red)={1, 2, 3, 4}

S(blue) = {1}

c) No, red die cannot be zero.

16. a) Yes, getting an A in statistics does not depend on getting an A in Biology.

b) 0.02275



Concepts 14

3.6 Basic Counting Rules

Answers

1. a) 4

b) 8

c) 16

d) 2n

2.

P(Black) = 1

12

Shirts Pants Socks

Black

White

Green

Black

Brown

Black

Brown

Black

Brown

Black

White

Black

White

Black

White

Black

White

Black

White

Black

White



Concepts 15

3.

P (at most 1 H) = 4 1

16 4or

H

T

H

T

H

T

H

T H

T

H

T

H

T

H

T

H

T H

T

H

T H

T H

T H

T H

T



Concepts 16

4. 90

5. 6

6. 130

7. a) 144

b) 504

8. 40

9. 2.09x1013

10. a)84

b) 14



Concepts 17

3.7 Permutations and Combinations Compared

Answers

1. 2598960

2. a) 5

b) 120

c) 84

d) 4368

3. 6

4. 20475

5. 491400

6. 3628800

7. Combination since the numbers are chosen, they are chosen without order. Notation:

49 6C

8. a) 30240

b) 720

9. a) 604800

b) 30240

10. Permutations and Combinations both make use of the factorial function. Permutations

are used when order matters. Combinations are used when order does not matter.

Date post:	23-Feb-2022
Category:	Documents
Upload:	others
View:	5 times
Download:	0 times

3.1 Sample Spaces and Events

Documents