ACE+ REVIEW CENTER

APRIL 2023 REVIEW PROGRAM

7. From a box containing 6 red balls, 8 white balls and 10 blue balls, one ball is
1. In how many ways can 6 distinct books be arranged in a bookshelf?
drawn at random. Determine the probability that it is red or white.
A. 720 B. 120
A. 1/3 B. 7/12
C. 360 D. 180
C. 5/12 D. 1/4

2. How many four-point digit can be formulated by the use of digits 1, 2, 3, 4,

5, and 7 if one digit is used only once in common? 8. From a bag containing 4 black balls and 5 white balls, two balls are drawn one
A. 260 B. 380 at a time. Find the probability that both balls are white. Assume that the
C. 480 D. 360 first ball is returned before the second ball is drawn.
A. 25/81 B. 16/81
C. 5/18 D. 40/81

3. How many different ways can 5 boys and 5 girls form a circle with boys and
girls alternate?
A. 28,800 B. 2,880 9. A fair coin is tossed three times. What is the probability of getting either
C. 5,600 D. 14,400 3 heads or 3 tails?
A. 1/8 B. 3/8
C. 1/4 D. 1/2

4. There are four balls of different colors. Two balls at a time are taken and
arranged any way. How many such combinations are possible?
A. 36 B. 3 10. The probability of getting a credit in an examination is 1/3. If three students
C. 6 D. 12 are selected at random, what is the probability that at least one of them got a
credit?
A. 19/27 B. 8/27
C. 2/3 D. 1/3

5. In how many ways can you invite one or more of your five friends in a party?
A. 15 B. 31
C. 36 D. 25
11. There are 3 questions in a test. For each question 1 point is awarded for a
correct answer and none for a wrong answer. If the probability that the student
correctly answers a question in the test is 2/3, determine the probability that
she gets zero in the test.
6. In how many ways can a committee of three consisting of two civil engineers A. 8/27 B. 4/9
and one electrical engineer can be formed from four civil engineers and three C. 1/30 D. 1/27
electrical engineers?
A. 18 B. 64
C. 32 D. 36
 ACE+ REVIEW CENTER
APRIL 2023 REVIEW PROGRAM

12. The probability of getting at least 2 heads when a coin is tossed four times
is
A. 11/16 B. 13/16 17. A construction company will hire 7 men and 4 women. In how many ways can the
C. 1/4 D. 3/8 company choose from 9 men and 6 women who qualified for the position?
A. 680 B. 540
C. 480 D. 840

18. There are 50 tickets in a lottery in which there is a first and second prize.
What is the probability of a man drawing a prize if he owns
13. Determine the probability of drawing either a king or a diamond in a single 5 tickets?
draw from a pack of 52 playing cards. A. 50% B. 25%
A. 2/13 B. 3/13 C. 20% D. 40%
C. 4/13 D. 1/13

19. Roll a pair of dice. What is the probability that the sum of two numbers
14. In how many ways can 4 boys and 4 girls be seated alternately in a row is 11?
of 8 seats? A. 1/36 B. 1/9
A. 1152 B. 2304 C. 1/18 D. 1/20
C. 576 D. 2204

20. Roll two dice once. What is the probability that the sum is 7?
15. In Math examination, a student may select 7 problems from a set of 10 A. 1/6 B. 1/8
problems. In how many ways can he make his choice? C. 1/4 D. 1/7
A. 120 B. 530
C. 720 D. 320

21. A card is drawn from a deck of 52 playing cards. Find the probability of
16. How many committees ca be formed by choosing 4 men from an organization of a drawing a king or a red card.
membership of 15 men? A. 0.5835 B. 0.5385
A. 1390 B. 1240 C. 0.3585 D. 0.8535
C. 1435 D. 1365

22. A face of a coin is either head or tail. If three coins are tossed, what is
the probability of getting three tails? 23. A bag contains 3 white and 5 black balls. If two balls are drawn in succession
A. 1/8 B. 1/2 without replacement, what is the probability that both balls are black?
C. 1/4 D. 1/6 A. 5/28 B. 5/16
C. 5/32 D. 5/14
24. The number of ways can 3 nurses and 4 engineers can be seated on a bench with 30. Six boys and four girls are to be seated on a bench. How many ways can they be
the nurses seated together is seated if the boys must be seated next to each other?
A. 144 B. 258 A. 86400 B.156240
C. 720 D. 450 C. 17280 D. 762048

25. How many ways can 6 persons line-up in any order? 31. Six boys and four girls are to be seated on a bench. How many ways can they be
A. 120 B. 60 seated if the boys must be seated side by side and also the girls?
C. 420 D. 720 A. 3628800 B. 156240
C. 34560 D. 17280

26. How many ways can 6 persons line-up if one person insists on standing in
front? 32. The captain of a chess team assigns himself to board 1. If there are six
A. 120 B. 720 players including the captain, how many ways can the team be assigned to the
C. 121 D. 6 boards if there are six chess boards.
A. 120 B. 720
C. 121 D. 6

27. How many ways can 6 persons line-up if two of those persons refuse to stand
next to each other?
A. 240 B. 120 33. A group of musicians is composed of three drummers, four pianists, and five
C. 480 D. 48 guitarists. How many ways can a trio be formed with 1 pianist, 1 drummer, and
1 guitarist?
A. 20 ways B. 60 ways
C. 40 ways D. 80 ways

28. Six boys and four girls are to be seated on a bench. How many ways can they be
seated in any order?
A. 3628800 B. 420 34. In how many ways can a PICE Chapter with 15 directors choose a President, a
C. 44100 D. 388260 Vice President, a Secretary, a Treasurer and an Auditor, if no member can hold
more than one position?
A. 360,360 B. 32,760
C. 3,003 D. 3,603,600

29. Six boys and four girls are to be seated on a bench. How many ways can they be
seated if the girls must be seated next to each other?
A. 17280 B. 120960
C. 604800 D. 156240 35. There are 8 pocket holes at the periphery of a round horizontal platform. In
how many ways can
8 balls of different colors be placed with one ball in each pocket?
A. 40320 B. 120
C. 8 D. 5040
36. How many numbers can we form from number 0, 1, 3, 4, 8 and 9 that are greater 42. To make a ham and cheese sandwich you are given a choice of 3 kinds of ham, 5
than 430? kinds of cheese, and 2 kinds of bread. How many different sandwiches can you
A. 48 B. 51 make?
C. 43 D. 60 A. 30 B. 40
C. 50 D. 60

37. Five different mathematics books, four different hydraulics books and two 43. How many ways can a person choose three of four colors for the purpose of
different structural books are to be placed in a shelf with the books of the painting the inside of a house?
same subject together. Find the number of ways in which the books can be A. 24 B. 12
placed. C. 6 D. 4
A. 292 B. 5760
C. 34560 D. 12870

44. How many ways can 6 representatives be selected from a class of 24 students?
A. 134596 B. 144
38. A college plays 12 football games during a season. In how many ways can the C. 665280 D. 96909120
team end the season with 7 wins, 3 losses, and 2 ties?
A.7920 B. 210
C.2520 D. 11880

45. How many ways can you invite any one or more of your eight friends to come to
your birthday party?
A. 255 B.455
39. In a certain city in the Philippines, all seven- digit telephone numbers begin C.155 D.100
with 350. How many telephone numbers may be assigned to that city if the last
four digits should not begin or end in zero?
A. 5040 B. 8100
C. 5184 D. 10000
46. A construction company will hire 10 skilled carpenters and 4 skilled masons.
In how many ways can the company choose from 18 carpenters and 6 masons who
are qualified for the position?
A. 675 B. 6648
C. 6735 D. 656370
40. How many telephone numbers if there's no restriction?
A. 5040 B. 8100
C. 840 D. 10000

47. How many ways can a student select a set of 4 Structural Design books and 3
Hydraulics books from a set of 9 Structural Design books and 5 Hydraulics
books?
41. How many telephone numbers if there's no repetition of digits?
A. 136 B. 1260
A. 5040 B. 5184
C. 485 D. 620
C. 840 D. 210
48. In how many ways can 14 employees be partitioned into 6 committees where 2 of 54. A password of a computer uses five digits where they are from 0 and 9. What is
the committees contain 3 men and the others 2? the probability that the password solely consists of prime numbers and zero?
A. 25, 225,200 B. 151,351, 200 A. 1/23 B. 1/2
C. 50,450,400 D. 302,702,400 C. 1/3 D. 1/32

49. It is required to seat 5 different men and 4 different women in so that the 55. The probability of event A happening is 3/5 and the probability of event B
women occupy the even places. How many arrangements are possible? happening is 2/3. What is the probability of only event A happening, i.e.
A. 20 B. 2880 event A happening and event B not happening?
C. 362880 D. 120 A. 1/5 B. 5/3
C. 3/5 D. 13/15

50. From 7 consonants and 5 vowels, how many words can be formed consisting of 4
56. In a family of five children, what is the chance that there are three boys and
different consonants and 3 different vowels? The words need not have meaning.
two girls?
A. 50,555 B. 3,991,600
A. 1/32 B. 1/10
C. 1,764,000 D. 4,500
C. 5/16 D. 3/5

51. An urn contains four black balls and six white balls. What is the probability
of getting one black ball and one white ball in two consecutive draws from the
urn? 57. How many line segments can be drawn from 9 distinct points?
A. 0.24 B. 0.53 A. 36 B. 81
C. 0.48 D. 0.07 C. 72 D. 9

58. The probability of event A happening is 3/5 and the probability of event B
52. A dart is randomly thrown at a circular dartboard with target circles having
happening is 2/3. What is the probability of either A or B, or A and B
radii of 1, 3, and 5. Find the probability that the dart lands on the shaded
happening.
circular region between 1 and 3. Assume that the dart will fall only within the
A. 1/5 B. 5/3
5 in radius.
C. 3/5 D. 13/15
A. 8/25 B. 1/3
C. 9/25 D. 1/2

59. A basketball player averages 65% in a free-throw line. What is the probability
of missing one or two free throws?
53. A janitor with a bunch of 9 keys is to open a door but only one key can
A. 0.455 B.0.8225
open. What is the probability that he will succeed in 3 trials?
C. 0.578 D.0.35
A. 0.333 B. 0.25
C. 0.5 D. 0.2
60. In a dice game, one fair die is used. The player wins P50.00 if he rolls either 65. Standard Deviation;
2 or 4. He loses P20.00 if he turns up any other faces. What is the expected A. 5 B. 10
winning for one roll of the die? C. 15 D. 17.078
A. P2.22 B. P3.33
C. P4.44 D. P5.55

66. Compute the standard deviation of the following set of numbers

2, 5, 6, 8, 11, and 15
61. In a dice game, one fair die is used. The player wins P20.00 if he rolls either A. 4.6224 B. 4.2197
1 or 6. He loses P10.00 if he turns up any other face. What is the expected C. 2.8462 D. 3.1178
winning for one roll of the die?
A. P 40.00 B. P 20.00
C. P 0.00 D. P 10.00

67. Given the following set of numbers arranged from smallest to largest: {x, 5,
3x, 12, 18, x^3-5}. If the range of the set is 19, what is the mean of the
set?
A. 11.5 B. 10.5
62. A contest offers the following cash prizes: Number of Prizes Prize Values
C. 12.5 D. 9.5
1 P 1,000,000
10 P 100,000
100 P 10,000
1000 P 1,000
If the sponsor expects 20 million contestants, find the expected value for a
single contestant. Situation – The table below shows a gamer's kills- to-death ratio for 12 random
A. 0.2 B. 0.5 games
C. 0.1 D. 0.6 6.4 5.5 6.8 4.9 5.6 3.8
3.8 4.8 6.4 5.0 4.2 3.8
Assume that the measurements are a simple random sample.

68. Calculate the sample mean for this data.

A. 5.025 B. 5.083
63. A game is played in which a coin is flipped one time. If the coin lands on
C. 4.981 D. 4.890
tails, the player wins $5. If the coin lands on heads, the player wins $10.
What is the expected value for a player who plays this game one time?
A. $9.00 B. $ 7.50
C. $10.50 D. $15.50

69. Calculate the sample median for this data

A. 4.9 B. 4.95
C. 5.0 D. 5.05
Situation – Toss a fair coin 100 times, and count the number of heads that appear.
Find the following:

64. Expected number of heads;

A. 25 B. 50 70. Calculate the sample mode for this data.
C. 75 D. 100 A. 3.8 B. 6.4
C. 4.9 D. 5.0
71. Calculate the range for this data. 77. Find the probability of getting between 3 and 6 heads inclusive in 10 tosses
A. 2 B. 3 of a fair coin by using the normal approximation to the binomial distribution.
C. 4 D. 5 A. 0.246 B. 0.445
C. 0.543 D. 0.772

72. Calculate the sample standard deviation and variance for this data.
A. 1.0286, 1.0581 B.2.0286, 2.0581 Situation – A coin is tossed 6 times.
C.1.055, 1.0854 D.2.055, 2.0681
78. What is the probability that exactly two heads occur?
A. 2 / 6 B. 15 / 64
C. 63 / 64 D. 11 / 32

73. Determine the expected number of boy in a family with 8 children, assuming the
sex distribution to be equally probable. What is the probability that the
expected number of boys does occur?
A. 0.212 B. 0.273 79. What is the probability of getting at least four heads?
C. 0.351 D. 0.405 A. 2 / 6 B. 15 / 64
C. 63 / 64 D. 11 / 32

74. A safety engineer claims that only 40% of all workers wear safety helmets when
they eat lunch at the workplace. Assuming that his claim is right, find the 80. What is the probability of no heads occur?
probability that 4 of 6 workers randomly chosen will be wearing their helmets A. 2 / 6 B. 15 / 64
while having lunch at the workplace. C. 63 / 64 D. 11 / 32
A. 0.13824 B. 0.12438
C. 0.14382 D. 0.18234

81. Two numbers are chosen at random from among the numbers 1 to 10 without
replacement. Find the probability that the second number chosen is 5.
75. When 100 coins are tossed, what is the probability that exactly 50 A. 15% B. 25%
are heads? C. 40% D. 10%
A. 0.0697 B. 0.0679
C. 0.0796 D. 0.0769

82. The UN forces of Bosnia use a type of missile that hits the target with a
probability of 0.3. How many missiles should be fired so that there is at
76. Smith and Jones, both 50% marksmen, decide to fight a duel in which they least 80% probability of hitting the target?
exchange alternate shots until one is hit. What are the odds in favor of the A. 2 B. 5
man who shoots first? C. 4 D. 3
A. 0.5 B. 0.3
C. 0.4 D. 0.8
 89. At most 2 will not fire.
83. There are 10 defects per 1000 items of a product in the long run. What is the A.0.9667 B.0.8867
probability that there is one and only one defective in a random lot of 100? C.0.1667 D.0.6677
A. 0.3697 B. 0.3796
C. 0.3967 D. 0.3679

Situation – A company producing electric relays has three manufacturing plants

producing 50, 30 and 20 percent, respectively, of its product. Suppose that the
84. There are six (6) bulbs in a house out of which probabilities, that relay manufactured by these plants is defective, are 0.02, 0.05,
3 are defective. If 2 bulbs are picked randomly, find the probability that at and 0.01, respectively.
least one is defective.
A. 0.2 B. 0.6 90. If relay is selected at random from the output of the company, what is the
C. 0.4 D. 0.8 probability that it is defective?
A. 0.027 B. 0.036
C. 0.033 D. 0.029

Situation – Five cards are drawn one at a time from an ordinary deck of 52 cards.

85. Find the probability that exactly two diamonds are drawn. 91. If a relay selected at random is found to be defective, what is the
A. 0.001116 B. 0.001006 probability that it was manufactured by plant 2?
C. 0.001016 D. 0.001666 A. 0.556 B. 0.666
C. 0.544 D. 0.356

86. Find the probability that exactly three red cards are drawn.
A. 0.066 B. 0.026
Situation – A supermarket manager knows that an average of four persons will pass
C. 0.016 D. 0.062
through the checkout line during any 10-minute period.

92. What is the probability of no customer in a 10- minute period?

A. 0.018 B. 0.426
87. Find the probability that at least one face card is drawn.
C. 0.135 D. 0.670
A. 0.7486 B. 0.7468
C. 0.7586 D. 0.7568

93. What is the probability of no customer in a 5- minute period?

A. 0.018 B. 0.426
Situation – From a lot of 10 missiles 4 are selected at random and fired. If the C. 0.135 D. 0.670
lot contains 3 defective missiles that will not fire, what is the probability that:

88. All 4 will fire.

A. 0.1429 B. 0.5
C. 0.3333 D. 0.1667
94. What is the probability of no customer in a 1- minute period?
A. 0.018 B. 0.426 100. What is the probability that a customer will spend more than 15 minutes in
C. 0.135 D. 0.670 the bank given that he is still in the bank after 10 minutes?
A. 0.604 B. 0.712
C. 0.865 D. 0.911

Situation – A delivery of ten items is received from a manufacturing plant at which

5% of the items produced are known to be defective.
Situation - The probability of a component failing in one year due to excessive
95. What is the probability of no defective items among the ten items? temperature is 1/20, that due to excessive vibration is 1/25 and that due to
A. 0.329 B. 0.303 excessive humidity is 1/50. Determine the probabilities that during a one-year
C. 0.549 D. 0.607 period a component

101. Fails due to excessive temperature and excessive vibration.

A. 0.002 B. 0.060
C. 0.521 D. 0.931
96. What is the probability of exactly one defective item?
A. 0.329 B. 0.303
C. 0.549 D. 0.607

Situation – Suppose the heights H of 800 students are normally distributed with 102. Fails due to excessive vibration or excessive humidity.
mean 66 inches and standard deviation 5 inches. Find the number N of students with A. 0.002 B. 0.060
heights: C. 0.521 D. 0.931

97. Between 65 and 70.

A. 64 B. 92
C. 186 D. 294
103. Will not fail because of both excessive temperature and excessive
humidity
A. 0.002 B. 0.060
C. 0.521 D. 0.931
98. Greater than or equal to 6 feet (72 inches)
A. 64 B. 92
C. 186 D. 294

Situation – A batch of 40 components contain 5 which are defective. If a component

is drawn at random from the batch and tested and then a second component is drawn
at random, calculate the probability of having one defective component, both
Situation – Suppose that amount of time one spends in a bank is exponentially
distributed with mean 10 minutes. 104. With replacement
A. 0.2188 B. 0.7656
99. What is the probability that a customer will spend more than 15 minutes in C. 0.2244 D. 0.7628
the bank?
A. 0.11 B. 0.22
C. 0.33 D. 0.44
105. Without replacement
A. 0.2188 B. 0.7656
C. 0.2244 D. 0.7628

Situation – The probability of a man hitting a target is 0.25.

106. If he fires 7 times, what is the probability of his hitting at least two?
A. 4547 / 8192 B. 4745 / 8192
C. 4457 / 8192 D. 4574 / 8192

107. How many times must he fire so that the probability of his hitting the
target at least one is greater than 2/3?
A. 2 B. 3
C. 4 D. 5

Situation – Suppose 300 misprints are distributed randomly throughout a book of

500 pages. Find the probability that a given page contains:

108. Exactly 2 misprints.

A. 0.1220 B. 0.1511
C. 0.1005 D. 0.0988

109. 2 or more misprints

A. 0.1220 B. 0.1511
C. 0.1005 D. 0.0988