Discrete Math
Exam Review 2
Name: _______________________
1. A bag contains 2 oranges, 3 grapefruits, and 1 tangerine. A piece of fruit is chosen from the
bag at random. What is the probability that a grapefruit will be chosen from the bag?
A.
1
3
B.
2
3
C. 1
D.
1
2
2. Jessica owns 4 red shirts, 2 blue shirts, and 3 white shirts. She chooses a shirt to wear at
random. What is the probability that she chooses a red shirt?
A.
1
2
B.
1
4
C.
4
9
D.
3
5
3. A number cube is rolled 25 times. A number less than four comes up 20 times. What is the
experimental probability that a number less than four is rolled?
A.
4
25
B.
4
5
C.
3
25
D.
1
2
4. A jar contains 5 black and 9 white marbles. Priscilla draws a marble from the jar. What is
the probability that she drew a black marble?
A.
5
14
B.
1
5
C.
5
9
D. 0
5. A coin is flipped 14 times, and it comes up heads 10 times. What is the experimental
probability that the coin comes up heads?
A.
1
14
B.
5
7
C.
1
10
D.
1
2
6. A coin is flipped 18 times and it comes up tails 12 times. What is the experimental
probability that the coin comes up tails?
A.
2
3
B.
4
5
C.
1
18
D.
1
12
7. Tim throws darts at a dartboard that has numbers 1 through 20 and a bull’s-eye 40 times, and
hits the bull’s-eye 16 times. What is the experimental probability that Tim hits the bull’s-eye?
A.
1
40
B.
1
16
C.
4
5
D.
2
5
8. Tim throws darts at a dartboard that has numbers 1 through 20 and a bull’s-eye 50 times, and
hits the bull’s-eye 10 times. What is the experimental probability that Tim hits the bull’s-eye?
A.
1
50
B.
1
10
C.
1
2
D.
1
5
9. A number cube is rolled 30 times, and a six comes up 5 times. What is the experimental
probability that a six is rolled?
A.
1
5
B.
1
6
C.
2
5
D.
1
30
10. A number cube is rolled 30 times, and a number less than four comes up 22 times. What is
the experimental probability that a number less than four is rolled?
A.
1
6
B.
4
15
C.
11
15
D.
1
22
11. A number cube is rolled 30 times and a number less than five comes up 20 times. What is
the experimental probability that a number GREATER than four is rolled?
A.
1
20
B.
2
3
C.
1
10
D.
1
3
12. A number cube is rolled 24 times, and a four is rolled 6 times. What is the experimental
probability that a four is NOT rolled?
A.
1
4
B.
1
6
C.
5
6
D.
3
4
13. A spinner used for a game is divided into 3 sections: yellow, brown, and orange. Janie spins
the spinner 18 times. The spinner lands on yellow 8 times. What is the experimental probability
that the spinner does NOT land on yellow?
A.
4
9
B.
5
9
C.
2
3
D.
1
4
14. A spinner used for a game is divided into 4 sections: yellow, brown, red, and orange. Janie
spins the spinner 20 times. The spinner lands on brown 6 times. What is the experimental
probability that the spinner does NOT land on brown?
1
3
7
4
B.
C.
D.
5
10
10
5
15. A jar contains 6 red and 8 blue marbles. A marble is drawn from the jar. What is the
probability that a red marble is drawn?
A.
A.
3
7
B.
3
4
C.
4
7
D.
1
6
16. A jar contains 4 red and 8 blue marbles. A marble is drawn from the jar. What is the
probability that a red marble is drawn?
A.
1
2
B.
1
3
C.
2
3
D.
1
4
17. A person is chosen at random from a room that contains 10 men and 6 women. What is the
probability that a woman is chosen?
A.
3
8
B.
3
5
C.
5
8
D.
1
2
18. A person is chosen at random from a room that contains 24 men and 26 women. What is the
probability that a woman is chosen?
A.
12
13
B.
12
25
C.
13
25
D.
13
50
19. Jess owns 4 red shirts, 2 blue shirts, and 3 white shirts. She chooses a shirt to wear at
random. What is the probability that she chooses a white shirt?
A.
2
9
B.
1
3
C.
4
9
D.
1
2
20. Jess owns 4 red shirts, 5 blue shirts, and 3 white shirts. She chooses a shirt to wear at
random. What is the probability that she chooses a white shirt?
A.
1
2
B.
5
12
C.
1
3
D.
1
4
21. A bag contains 4 oranges, 3 grapefruits, and 8 tangerines. A piece of fruit is chosen from the
bag at random. What is the probability that a grapefruit is NOT chosen?
A.
1
5
B.
1
4
C.
3
4
D.
4
5
22. A bag contains 6 oranges, 10 grapefruits, and 8 tangerines. A piece of fruit is chosen from
the bag at random. What is the probability that a grapefruit is NOT chosen?
A.
5
12
B.
2
7
C.
7
12
D.
5
7
23. A fair number cube is rolled. What is the probability that a number greater than four is
rolled?
A.
1
3
B.
2
3
C.
1
2
D.
1
6
24. A fair number cube is rolled. What is the probability that an odd number is rolled?
A.
1
3
B.
1
2
C.
1
6
D. 1
25. A card is chosen at random from a deck of 52 cards. It is replaced and a second card is
chosen. What is the probability of choosing a King and an Ace?
A.
1
26
B.
2
13
C.
1
169
D.
1
13
26. A number cube is rolled and a coin is tossed. What is the probability of the coin landing on
tails and rolling a six on the number cube?
A.
1
12
B.
1
4
C.
1
3
D.
1
6
27. A coin is tossed and a spinner numbered 1 to 7 is spun. What is the probability of getting an
even number and tails?
A.
2
7
B.
4
9
C.
1
3
D.
3
14
28. Three cards are chosen from a standard deck of 52 playing cards with replacement. What is
the probability every card will be a heart?
A.
1
4
B.
1
64
C.
1
13
D.
3
4
29. A spinner numbered 1 to 6 is spun twice. What is the probability of getting a 4 on the first
spin and an even number on the second spin?
A.
1
12
B.
1
4
C.
2
3
D.
1
6
30. Two number cubes are rolled. What is the probability that the sum of the numbers rolled is
either a 7 or an 11?
A.
1
4
B.
5
18
C.
2
9
D.
1
2
31. A bag contains 8 blue marbles, 6 red marbles, and 4 green marbles. What is the probability
of selecting a blue marble, replacing it in the bag and then selecting a red marble?
A.
7
9
B.
1
3
C.
2
27
D.
4
27
32. Two number cubes are rolled. What is the probability that the sum of the numbers rolled is
either a 3 or an 8?
A.
7
36
B.
1
6
C.
5
648
D.
1
144
33. A bag contains 3 red marbles, 2 blue marbles ,and 5 green marbles. What is the probability
of selecting a red marble, replacing it in the bag and then selecting a green marble?
A.
7
10
B.
4
5
C.
3
20
D.
1
10
34. A five-sided solid has the numbers 1, 2, 3, 4, and 5. What is the probability of rolling two
five-sided number solids and getting a sum of either a 4 or an 8?
A.
6
625
B.
9
625
C.
6
25
D.
1
5
35. A card is chosen at random from a deck of 52 cards. It is replaced and a second card is
chosen. What is the probability both cards will be an Ace?
A.
1
169
B.
2
13
C.
1
26
D.
1
13
36. A number cube is rolled and a coin is tossed. What is the probability of the coin landing on
tails and rolling a six on the number cube?
A.
1
3
B.
1
`
4
C.
1
6
D.
1
12
37. A coin is tossed and a spinner numbered 1 to 7 is spun. What is the probability of getting an
odd number and heads?
A.
2
7
B.
4
9
C.
1
3
D.
3
14
38. Three cards are chosen from a standard deck of 52 playing cards without replacement. What
is the probability every card will be an Ace?
A.
1
13
B.
1
64
C.
1
2197
D.
1
169
39. A spinner numbered 1 to 6 is spun twice. What is the probability of getting a 3 on the first
spin and an odd number on the second spin?
A.
1
12
B.
1
4
C.
2
3
D.
1
6
40. Two number cubes are rolled. What is the probability that the sum of the numbers rolled is
either a 6 or an 8?
A.
1
4
B.
5
18
C.
2
9
D.
1
2
41. A bag contains 8 blue marbles, 6 red marbles, and 4 green marbles. What is the probability
of selecting a red marble, replacing it in the bag and then selecting a green marble?
A.
7
9
B.
1
3
C.
2
27
D.
4
27
42. Two number cubes are rolled. What is the probability that the sum of the numbers rolled is
either a 4 or a 10?
A.
7
36
B.
1
6
C.
5
648
D.
1
144
43. A bag contains 3 red marbles, 2 blue marbles and 5 green marbles. What is the probability
of selecting a blue marble, replacing it in the bag and then selecting a green marble?
A.
7
10
B.
4
5
C.
3
20
D.
1
10
44. A five-sided solid has the numbers 1, 2, 3, 4, and 5. What is the probability of rolling two
five-sided number solids and getting a sum of either a 3 or an 8?
A.
6
625
B.
9
625
C.
6
25
D.
1
5
45. A bag contains 4 red marbles and 5 blue marbles. What is the probability of randomly
selecting a blue marble and then, without replacing it, selecting a red marble?
A.
5
18
B.
40
81
C.
16
81
D.
1
6
46. A bag contains 16 red marbles and 10 blue marbles. If two marbles are chosen at random,
one at a time without replacement, what is the probability of getting two red marbles?
A.
1
65
B.
9
65
C.
24
65
D.
64
169
47. Dianna has 4 quarters, 3 dimes, and 3 nickels in her purse. She reaches into her purse and
randomly grabs two coins, one at a time. What is the probability of first picking a dime and then,
without replacing it, selecting a nickel?
A.
7
10
B.
2
15
C.
1
10
D.
1
30
48. Two cards are randomly chosen from a standard deck of 52 playing cards without
replacement. What is the probability both cards will be hearts?
A.
8
663
B.
1
17
C.
3
663
D.
2
16
49. A sock drawer has 8 blue socks and 6 black socks. If I randomly select two socks, one at a
time, what is the probability I will first get a blue sock and then, without replacing it, a black
sock?
A.
24
91
B.
2
7
C.
6
81
D.
4
13
50. A bag contains 5 blue marbles, 6 red marbles, and 9 green marbles. Two marbles are drawn
at random, one at a time and without replacement. What is the probability of selecting two blue
marbles?
9
3
1
11
A.
B.
C.
D.
20
19
20
38
51. A bag contains 5 blue marbles, 6 red marbles, and 9 green marbles. Two marbles are drawn
at random, one at a time. What is the probability of selecting a green marble and then, without
replacing it, a red marble?
A.
9
38
B.
9
190
C.
27
190
D.
3
38
52. 10 cards are numbered from 1 to 10 and placed in a box. One card is selected at random and
is not replaced. Another card is then randomly selected. What is the probability of selecting two
prime numbers?
A.
2
15
B.
4
18
C.
7
90
D.
1
10
53. A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability
of randomly selecting a red marble then, without replacing it, randomly selecting a green
marble?
1
1
7
4
A.
B.
C.
D.
9
6
10
5
54. Two friends are taking an English class that has a monthly reading list. Once a student
chooses a book from the list, no other student can choose that book. If there are 3 mystery and 4
romance books left, what is the probability that the first friend will randomly select a mystery
book and the second friend will randomly select a romance book?
A.
16
49
B.
1
7
C.
2
7
D.
12
49
55. A bag contains 4 red marbles and 5 blue marbles. If two marbles are chosen at random, one
at a time and without replacement, what is the probability of getting two red marbles?
A.
5
18
B.
40
81
C.
16
81
D.
1
6
56. A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at
random, one at a time and without replacement, what is the probability of getting tow green
marbles?
9
1
45
64
A.
B.
C.
D.
196
91
169
65
57. DeAnna has 4 quarters, 3 dimes, and 3 nickels in her purse. She reaches into her purse and
randomly grabs two coins, one at a time. What is the probability DeAnna will first grab a quarter
and then, without replacing it, grab a nickel?
A.
7
10
B.
2
15
C.
1
10
D.
1
30
58. Two cards are randomly chosen, one at a time, from a standard deck of 52 playing cards
without replacement. What is the probability both cards will be an Ace?
A.
8
663
B.
1
17
C.
1
221
D.
2
16
59. A sock drawer has 8 blue socks and 6 black socks. A sock is chosen at random. Then,
without replacing that sock, another sock is chosen at random. What is the probability of
choosing two blue socks?
A.
24
91
B.
2
7
C.
6
81
D.
4
13
60. A bag contains 5 blue marbles, 6 red marbles, and 9 green marbles. Two marbles are drawn
at random. What is the probability of first drawing a blue marble and then, without replacing it,
drawing a red marble?
A.
9
20
B.
3
38
C.
1
19
D.
11
20
61. A bag contains 5 blue marbles, 6 red marbles, and 9 green marbles. Two marbles are drawn
at random, one at a time and without replacement. What is the probability of selecting two red
marbles?
9
3
1
11
A.
B.
C.
D.
20
19
20
38
62. 10 cards are numbered from 1 to 10 and placed in a box. One card is selected at random and
is not replaced. Another card is then randomly selected. What is the probability of selecting two
numbers that are less than 6?
A.
2
9
B.
5
18
C.
1
5
D.
1
4
63. A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability
of randomly selecting a blue marble, then without replacing it, randomly selecting a green
marble?
1
1
7
4
A.
B.
C.
D.
9
6
10
5
64. Two friends are taking an English class that has a monthly reading list. Once a student
chooses a book from the list, no other student can choose that book. If there are 3 mystery and 4
romance books left, what is the probability that both friends randomly select a romance book,
one after the other?
A.
16
49
B.
1
7
C.
2
7
D.
12
49
65. Evaluate the expression. Choose the best answer. 7!
A. 840
B. 720
C. 40,320
D. 5,040
66. Evaluate the expression. Choose the best answer. 11!
A. 40,320
B. 362,880
C. 3,628,800
D. 39,916,800
67. Evaluate the expression. Choose the best answer. 9!
A. 5,040
B. 362,880
C. 326,880
68. Evaluate the expression. Choose the best answer. 5!
A. 220
B. 120
C. 720
D. 820
D. 40,320
69. Evaluate the expression. Choose the best answer. 4!5!6!
A. 86,424
B. 120,840
C. 86,394
D. 85,424
70. Evaluate the expression. Choose the best answer. 8!6!3!
A. 44,640
B. 42,640
C. 40,320
D. 41,046
71. Evaluate the expression. Choose the best answer. 9!6!
A. 362,160
B. 362,880
C. 363,600
D. 362,610
72. Evaluate the expression. Choose the best answer. 7!4!6!
A. 120,240
B. 120,020
C. 120,000
73. Evaluate the expression. Choose the best answer.
A. 840
B. 120
C. 210
B. 6,480
B. 65
C. 120
B. 876
B. 30,240
B. 336
8 P3
D. 336
10 P8
C. 1,814,400
78. Evaluate the expression. Choose the best answer.
A. 8,765
6 P2
C. 1,680
77. Evaluate the expression. Choose the best answer.
A. 604,800
D. 648
D. 30
76. Evaluate the expression. Choose the best answer.
A. 6,720
9!
3!
C. 60,480
75. Evaluate the expression. Choose the best answer.
A. 360
7!
4!
D. 2,520
74. Evaluate the expression. Choose the best answer.
A. 30,240
D. 119,420
D. 3,628,800
8 P4
C. 1,680
D. 20,160
79. A college questionnaire was distributed among high school students asking each student to
rank the items he or she would like to learn more about. There are five items: financial aid,
tuition, class schedule, dormitories, and cost of books. In how many ways can the student
answer this questionnaire?
A. 720 ways
B. 25 ways
C. 120 ways
D. 5,040 ways
80. A college questionnaire was distributed among high school students asking each student to
rank the items he or she would like to learn more about. There are six items: financial aid,
tuition, class schedule, dormitories, student organizations, and cost of books. In how many ways
can the student answer this questionnaire?
A. 5,040 ways
B. 120 ways
C. 720 ways
D. 36 ways
81. A home alarm system randomly assigns a four-character code for each person. The code
will not repeat a character. The characters are 2, 3, 4, 5, M, V, T, or R. What is the total number
of codes that can be randomly assigned?
A. 6,720 codes
B. 1,680 codes
C. 336 codes
D. 20,160 codes
82. A home alarm system randomly assigns a five-character code for each person. The code
will not repeat a character. The characters are 0, 1, 2, 3, 4, 5, M, V, T, G, Y, or R. What is the
total number of codes that can be randomly assigned?
A. 1,320 codes
B. 95,040 codes
C. 9,540 codes
D. 11,880 codes
83. The neighborhood association sent a survey asking families to rank their concerns for the
neighborhood. The four items listed were crime, recycling, speeding, and trash collection. In
how many ways can a family answer this survey?
A. 120 ways
B. 16 ways
C. 48 ways
D. 24 ways
84. The neighborhood association sent a survey asking families to rank their concerns for the
neighborhood. The eight items listed were crime, recycling, speeding, pool safety, noise,
parking, graffiti, and trash collection. In how many ways can a family answer this survey?
A. 120 ways
B. 720 ways
C. 5,040 ways
D. 40,320 ways