A1© 2015 College Board. All rights reserved. SpringBoard Geometry, Unit 6 Practice

LeSSon 38-1

1. a. 25

b. 35

c. 720

d. 1320

e. 14

2. a. 111, 112, 113, 121, 122, 123, 131, 132, 133,

211, 212, 213, 221, 222, 223, 231, 232, 233,

311, 312, 313, 321, 322, 323, 331, 332, 333

b. 49

; Sample answer: Of the 27 outcomes listed,

12 of them have exactly one “1.”

3. a. P(even) 5 25

b. P(not even) 5 35

c. P(2) 5 15

d. P(not 2) 5 45

e. P(less than 6) 5 55

5 1

4. D

5. 38

LeSSon 38-2 6. a. HA, HB, HC, HD, TA, TB, TC, TD

b. 18

c. 58

d. 38

e. 78

7. B

8. a.

Grade 9 Grade 10 Grade 11 Total

Smart phone

28 32 45 105

not a smart phone

9 16 20 45

Total 37 48 65 150

b. 2837

c. 60105

47

5

d. 1

9. a. 62125

b. 3125

c. 117125

d. 60125

e. 122125

5 0.976

10. a. 18

b. 38

LeSSon 39-1 11. a. 110

b. 303

c. 98

d. 95

e. 47

12. a. 95350

5 1970

b. 98350

5 725

c. 110350

51135

d. 303350

e. 47350

Answers to Geometry Unit 6 Practice

A2© 2015 College Board. All rights reserved. SpringBoard Geometry, Unit 6 Practice

13. a. 0.65

b. 0.66

c. 0.22

d. It is the probability that a student does not have an after-school activity AND does not come to school by bus.

14.

290

P B

85

450

25

50

15. B

LeSSon 39-2 16. a. m, n, p

b. n

c. p, q

d. m, q

e. 1

17. a. Sample answer: the complement of S

b. Sample answer: R ¯ S and not R ˘ S

c. Sample answer: the complement of R ¯ S

d. Sample answer: R ˘ S or the complement of R ¯ S

e. Sample answer: the complement of R

18. a. 0.6

b. 0.1

c. 0.4

d. 0.8

19. A

20. a. 0.04

b. 0.22

LeSSon 40-1 21. A

22. 0.32

23. a. Sample answer: It is the probability of the complement of A¯B.

b. 0.26

c. 0.36

d. 0.25

24. a. Sample answer: I used P(A¯C) 5 P(A) 1 P(C) 2 P(A˘C). I know that P(A¯C) 5 0.85 since 0.85 is 1 2 0.15. Then,

0.85 5 0.57 1 0.38 2 P(A˘C)

0.85 5 0.95 2 P(A˘C)

P(A˘C) 5 0.95 2 0.85 5 0.10.

b.

0.47

A C

0.28

0.15

0.10

25. 0.31

LeSSon 40-2 26. D

27. 14

28. 0.83. Sample answer: Having lunch in the cafeteria and in an activity room are mutually exclusive events because the same student cannot have lunch in two different places at once. I can use the formula P(A¯B) 5 P(A) 1 P(B), so P(A¯B) 5 0.55 + 0.28 5 0.83.

29. a. 0.85

b. 0

c. 0.53

d. 0.62

e. 0.15

30. No. Sample answer: If A and B are mutually exclusive, then P(A¯B) 5 P(A) 1 P(B) 5 0.41 1 0.43 5 0.84. But we are told that P(A¯B) has a different value, namely, 0.81. Therefore A and B are not mutually exclusive. In fact, P(A˘B) 5 0.03.

A3© 2015 College Board. All rights reserved. SpringBoard Geometry, Unit 6 Practice

LeSSon 41-1

31. a. 2770

. Sample answer: There are a total of 27 cats

and a total of 70 pets.

b. 2543

. Sample answer: Of the 43 dogs, 25 of them

are on the second floor.

c. Sample answer: The problem can be stated as “Calculate the probability that a pet is on the second floor, given that the pet is a dog.”

32. C

33. a. 50260

5 526

b. 50180

5 518

c. 0150

05 d. 210260

2126

5

34. a. 55140

1128

5 b. 25110

522

5

35. Sample answer: If P(A | B) 5 0, then for all the outcomes that satisfy event B, none of them also satisfies event A. The conclusion that events A and B are mutually exclusive can be made.

LeSSon 41-2 36. C

37. a. P(B | A) 5 ∩P B AP A( )( )

b. 0.250.63

5 0.40

c. P(A | B) 5 ∩P A B

P B( )( )

d. 0.250.48

5 0.52

38. Find the probability that both R and T will happen, and divide that by the probability that T will happen.

39. a. P(X | Y) 5 0.20.4

5 12

b. P(Y | X) 5 0.20.6

5 13

c. lesser

d. Sample answer: P(X | Y) and P(Y | X) have the same numerator, P(X˘Y). Their denominators are P(Y) and P(X), and if P(Y) , P(X), then P(X | Y) . P(Y | X).

40. a. 425535

¯ 0.79 b. 80190

¯ 0.42

c. 80355

¯ 0.23 d. 425700

¯ 0.61

e. You need the row totals when the probability is “given that it is afternoon” or “given that it is evening.” You need the column totals when the probability is “given that it is a text message” or “given that it is a voice message.”

LeSSon 41-3 41. m 1 n 5 1

42. a. r is 150 times m, and s is 150 times n.

b. r 1 s 5 150

43. a. 48. It is (60)(0.8). b. 0.2. It is 1 2 0.8.

c. 12. It is (60)(0.2). d. 140. It is (200)(0.7).

e. 0.4. It is 1 2 0.6.

44. C

45. a. blue

blue

lavender

lavender

yellow

yellow

619

720

620

720

619

719

519

719

719

619

719

619

blue

lavender

yellow

blue

lavender

yellow

b. 620

? 519

5 338

LeSSon 42-1 46. D

47. a. No. P(A ˘ B) 5 0.16, so events A and B can both happen at the same time.

b. Yes. P(A) ? P(B) 5 (0.64 1 0.16) ? (0.16 1 0.04) 5 (0.8)(0.2) 5 0.16 5 P(A ˘ B). Since P(A)? P(B) 5 P(A ˘ B), events A and B are independent.

A4© 2015 College Board. All rights reserved. SpringBoard Geometry, Unit 6 Practice

48. a. P(S) 5 57

? 27

1 27

? 47

5 1049

1 849

5 1849

b. P(SC) 5 57

? 57

1 27

? 37

5 2549

1 649

5 3149

c. 27

d. No. P(S) fiP(S | D)

49. a. There are 60 pets and 30 dogs, so P(dog) 5 12

.

b. P(dog | second floor) 5 ∩P D

P( secondfloor)

(secondfloor)

5 15 /6035 /60

5 37

.

c. Independent. P(D) 5 P(D | second floor), so the events are independent.

d. P(C) 5 3060

5 12

.

P(C | first floor) 5 ∩P C

P( first floor)

(first floor) 5

10/6025/60

5 25

. The events are not independent.

50. a. Sample answer: Compare P(M ˘ N) with P(M) ? P(N). If the values are equal, events M and N are independent.

b. Find P(M) and P(M | N). If the probabilities are equal, events M and N are independent.

LeSSon 42-2 51. a. π14

72 ¯ 0.61

b. 1 2 0.61 5 0.39

52. a. 13

b. 38

c. 56

d. a360

53. D

54. a. π−a a

a4

4

2 2

2 5 π−4

4 5 −1

4p

b. Use the complement, whose probability is

1 2 (1 2 4p ) 5

4p

.

c. πb b

b16 4

(4 )

2 2

2

2 5

π )bb

4 (416

2

2

2 5

π442

5 π

14

2

d. The probability is the same for each target.

55. a. 1 3 4 3 9

361 1 1 1

5 2036

5

59

b. + +1 4 936

5 1436

5 718

c. 12436

5 89

d. 336

? 336

5 1

144

LeSSon 42-3

56. a. 4!2!

5 12

b. 11! 5 39,916,800

c. 10!

2!2!3! 5 151,200

d. 11!

4!4!2! 5 34,650

57. a. 26 ? 26 ? 10 ? 10 ? 10 5 676,000

b. 26 ? 25 ? 10 ? 9 ? 8 5 468,000

58. B

59. 15C3 5 15!3!12!

5 455 ways

60. a. 6C3 5 6!3!3!

5 20 ways

b. 8C3 5 8!3!5!

5 56 ways

c. 10C3 5 10!3!7!

5 120 ways

d. 6 ? 8 ? 10 5 480 ways