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Practice Problems IN Probability
BS Civil Engineering (Mindanao State University - Iligan Institute of Technology)
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1.
A man has 3 jackets, 10 shirts, and 5 pairs of slacks. If an outfit consists
of a jacket, a shirt, and a pair of slacks, how many different outfits can
the man make?
D. 150
A. 18
B. 30
C. 100
Probability
17. Industrial engineers are timing to workers to rank their speed at
assembling computers. There are 10 workers. How many different
permutations are possible?
D. 3628800
A. 864000
B. 86400
C. 362880
_____
18. The Engineering club at Midwestern University is to select a
president, a vice president, and a secretary/treasurer from 38
members of the club. How many ways to select them.
B. 50,616
C. 8,436
D. 1771,560
A. 73,815
_____
19. You know that the extension of a private telephone number is 272 but
you have forgotten the last 4 digits. You can only recall that the last 4
digits are 3, 6, 8, and 9 but you do not know the order. What is the
maximum number of telephone calls you will need to make in order
to dial the correct number?
A. 20
B. 24
C. 28
D. 32
_____
20. How many ways can 6 persons line-up If one person insists to stand
in front?
C. 120
D. 140
A. 80
B. 100
_____
21. In how many different ways can one make a first, second, third, and
fourth choice among 10 firms leasing construction equipment?
A. 3024
B. 5040
C. 3360
D. 4210
_____
22. The Beau Chene Garden Club has 12 members. They plan to elect a
president, a vice-president, and a treasurer. How many different
outcomes are possible for the election if each member is eligible for
each office and no one can hold two offices?
B. 1320
C. 2130
D. 2310
A. 1230
_____
23. In how many ways can a PICE chapter with 12 directors choose a
president, a vice-president, a secretary, a treasurer, and an auditor, if
no member can hold more than one position?
B. 95040
C. 665280
D. 845
A. 792
_____
24. Determine the number of different words of 5 letters each that can be
formed with the letters of the word chromate if each letter is used not
more than once.
D. 6720
A. 2670
B. 2760
C. 6270
_____
25. How many numbers may be formed by using 4 out of the 5 digits 1, 2,
3, 4, 5 if the digits must not be repeated in any order?
A. 120
B. 130
C. 140
D. 150
_____
26. How many 4-digit numbers may be formed with the 10 digits, 0, 1, 2,
3, …, 9 if each digit is used only once in each number?
C. 4536
D. 5634
A. 3456
B. 4563
_____
27. It is required to seat 5 men and 4 women in a row so that the women
occupy the even places. How many such arrangements are possible?
D. 2880
A. 120
B. 210
C. 280
_____
28. In how many ways can 9 different books be arranged on a shelf so that
3 of the books are always together,
A. 4230
B. 4320
C. 30240
D. 30420
_____
29. Six different biology books, 5 different chemistry books and 2
different physics books are to be arranged on a shelf so that the
biology books stand together, the chemistry books stand together,
and the physics books stand together. How many such arrangements
are possible?
A. 1036800 B. 1306800 C. 1360800 D. 1368000
_____
30. In how many ways can 3 boys and 2 girls sit in a row?
A. 48
B. 84
C. 100
D. 120
_____
31. 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. 120960
B. 34560
C. 86400
D. 94350
_____
32. The number of ways can 3 nurses and 4 engineers be seated on a
bench with the nurses seated together is?
C. 720
D. 450
A. 144
B. 258
_____
33. Five men and 3 women are to be seated on a bench. How many ways
can they be seated if the men must be seated side-by-side, and also
the women?
B. 1440
C. 2016
D. 4032
A. 720
_____
2. A student has a choice of 5 foreign languages and 4 sciences. In how
many ways can he choose 1 language and 1 science?
A. 9
B. 10
C. 18
D. 20
_____
3. There are 4 candidates for president of a club, 6 for vice-president and
2 for secretary. In how many ways can these three positions be filled?
A. 12
B. 18
C. 24
D. 48
_____
4. Peter is going to set up a stereo system by purchasing separate
components. There are 5 different receivers, 8 different DVD players,
and 12 different speaker systems. If Peter wants one of each of these
components, how many different stereo systems are possible?
B. 480
C. 540
D. 620
A. 360
_____
5. Next semester you are planning to take three courses—math, English,
and humanities. Based on time blocks and highly recommended
professors, there are 8 sections of math, 5 of English, and 4 of
humanities that you find suitable. Assuming no scheduling conflicts,
how many different three-course schedules are possible?
A. 17
B. 140
C. 160
D. 180
_____
6. A music school produced a number of musicians which includes 3
drummers, 4 trumpet players and 5 pianists. How many different jazz
trios can be formed from this batch of musicians if each trio consists
of a drummer, a trumpet player and a pianist?
A. 50
B. 60
C. 70
D. 80
_____
7. There are three flights from Houston to Chicago, four flights from
Chicago to Memphis and five flights from Memphis to Atlanta. How
many choices of flights include the Houston-Chicago-MemphisAtlanta connection?
C. 60
D. 150
A. 12
B. 120
_____
8. To make a ham and cheese sandwich you are given a choice of 3 kinds
of ham, 5 kinds of cheese, and 2 kinds of bread. How many different
sandwiches can you make?
A. 30
B. 10
C. 15
D. 45
_____
9. How many seven-digit local telephone numbers can be formed if the
first three digits are 279?
A. 3024
B. 6561
C. 5040
D. 10000
_____
10. In a certain city in the Philippines, all seven-digit telephone numbers
begin with 350. How many telephone numbers maybe assigned to
that city if the last four digits should not begin or end in zero?
B. 8100
C. 8800
D. 9200
A. 7980
_____
11. The LTO issues license plates consisting of letters and numbers. There
are 26 letters may be repeated. There are 10 digits and the digits may
be repeated. How many possible license plates can be issued with two
letters followed by three numbers?
A. 746,000 B. 864,000 C. 676,000 D. 542,000
_____
12. In how many ways can 2 different prizes be awarded among 10
contestants if both may not be give to the same person?
A. 19
B. 45
C. 90
D. 100
_____
13. In how many different orders may 5 persons be seated in a row?
C. 120
D. 3125
A. 24
B. 25
_____
14. In how many ways can 7 books be arranged on a shelf?
A. 4005
B. 5050
C. 5040
D. 5400
_____
15. Twelve different pictures are available, of which 4 are to be hung in a
row. In how many ways can this be done?
A. 11 880
B. 12 800
C. 13 660
D. 14 600
_____
16. An electronic controlling device requires six identical memory chips.
In how many ways can this mechanism be assembled using six given
chips?
A. 720
B. 540
C. 360
D. 840
_____
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34. In how many ways can 5 persons be seated at a round table?
A. 24
B. 48
C. 72
D. 120
_____
35. In how many ways can 8 persons be seated at a round table if 2
particular persons must always sit together?
C. 1440
D. 1360
A. 720
B. 680
_____
36. In how many ways can 4 men and 4 women be seated at a round table
if each woman is to be between two men?
D. 576
A. 12
B. 144
C. 288
_____
37. A group of engineers are taking their dinner in a big circular table. The
group is composed of 4 Civil Engineers, 3 Mechanical Engineers, 2
Electrical Engineers, and 2 Electronics and Communications
Engineers. How many arrangements can they form if the awesome
CE’s want to be together side by side?
A. 17280
B. 2880
C. 30240
D. 20160
_____
38. There are 3 copies each of 4 different books. In how many different
ways can they be arranged on a shelf?
A. 366 900 B. 369 600 C. 396 600 D. 390 660
_____
39. The Court of Appeals has 9 justices. On a certain case, the justices
voted 5 to 4 in favor of the defendant. In how many ways could this
have happened?
B. 126
C. 134
D. 140
A. 120
_____
40. How many permutations can be made from the letters of the word
ENGINEERING?
A. 39,916,800 B. 277,200 C. 55,440
D. 3,326,400
____
Probability
51. In 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?
B. 1260
C. 1420
D. 1580
A. 1080
_____
52. A semiconductor company will hire 7 men and 4 women. In how many
ways can the company choose from 9 men and 6 women who qualified
for the position?
D. 540
A. 680
B. 840
C. 480
_____
53. In a random draw of five cards from a deck of 52 playing cards, how
many ways can five red cards be drawn?
A. 32890
B. 2598960 C. 1287
D. 65780
_____
54. In a random draw of five cards from a deck of 52 playing cards, how
many cards can be drawn consisting three aces and 2 face cards?
B. 264
C. 426
D. 462
A. 246
_____
55. In how many ways can a person choose 1 or more of 4 electrical
appliances?
A. 15
B. 16
C. 17
D. 18
_____
56. How many ways can you invite any one or more of your eight friends
to come in your birthday party?
A. 255
B. 243
C. 128
D. 356
_____
57. An amusement park has 20 different rides. How many different
combinations of rides you can go on if you want to ride at least 15 of
them?
A. 21,700
B. 6196
C. 15,504
D. 32,767
_____
58. In how many ways can a teacher choose one or more students from
six eligible students?
A. 36
B. 46
C. 63
D. 64
_____
59. How many signals can be made with 5 different flags by raising them
any number at a time?
A. 235
B. 253
C. 325
D. 352
_____
60. Four different colored flags can be hung in a row to make coded signal.
How many signals can be made if a signal consists of the display of one
or more flags?
A. 64
B. 66
C. 68
D. 62
_____
61. Without repeating any digit, how many 3-digit numbers can you make
out from digits 0, 1, 3, 4, 8, 9 that are greater than 480
A. 47
B. 50
C. 80
D. 120
_____
62. Without repeating any digit, how many 3-digit numbers can you make
out from digits 0, 2, 3, 5, 7, 9 that are less than 730.
C. 68
D. 72
A. 60
B. 64
_____
63. How many ways can 6 persons line-up if two of those persons refuse
to stand next to each other?
A. 480
B. 520
C. 360
D. 440
_____
64. In how many ways can 5 people line up to pay their electric bills, if
two particular persons refuse to follow each other?
B. 72
C. 90
D. 140
A. 120
_____
65. A delegation of 4 students is selected each year from a college to
attend the National Student Association annual meeting. In how many
ways can the delegation be chosen if there are 12 eligible students
ways but two will not attend the meeting together?
A. 210
B. 240
C. 450
D. 540
_____
66. From a group of 20 volunteers, you are choosing at least 18 to be peer
counselors. In how many ways can this be done?
A. 120
B. 190
C. 210
D. 211
_____
67. In how many ways can a hostess select six luncheon guests from 10
women if she is to avoid having two of them together at the luncheon?
A. 210
B. 84
C. 140
D. 168
_____
68. In how many ways can we seat 7 people in a round table with a certain
3 people not in consecutive order?
A. 576
B. 3960
C. 5320
D. 689
_____
41. How many distinct permutations can be formed from all the letters of
the word sociological?
A. 9972900 B. 9997200 C. 99297200 D. 9979200
_____
42. How many different signals, each consisting of 6 flags hung in a
vertical line, can be formed from 4 identical red flags and 2 identical
blue flags?
A. 14
B. 28
C. 48
D. 72
_____
43. How many different sets of 4 students can be chosen out of 17
qualified students to represent a school in a mathematics contest?
A. 2380
B. 2830
C. 3280
D. 3820
_____
44. In how many ways can 5 styles be selected out of 8 styles?
A. 52 ways B. 54 ways C. 56 ways D. 58 ways
_____
45. Ayala Corporation advertised to hire financial analyst. The company
received applications from 10 candidates who seem to be equally
qualified. The company manager has decided to call only 3 candidates
for an interview. If she randomly selects 3 candidates from the 10,
how many total selections are possible?
B. 120
C. 130
D. 140
A. 110
_____
46. Determine the number of different triangles which can be formed by
joining the six vertices of a hexagon, the vertices of each triangle being
on the hexagon.
C. 20
D. 25
A. 10
B. 15
_____
47. In how many ways can 3 women be selected out of 15 women if 1 of
the women is to be included in every selection,
A. 81
B. 91
C. 101
D. 111
_____
48. From 6 chemists and 5 biologists, a committee of 7 is to be chosen so
as to include 4 chemists. In how many ways can this be done?
A. 120
B. 135
C. 150
D. 175
_____
49. Given 8 consonants and 4 vowels, how many 5-Ietter words can be
formed, each word consisting of 3 different consonants and 2
different vowels?
A. 20 430
B. 30 240
C. 40 320
D. 43 200
_____
50. In a random draw of four cards from a deck of 52 playing cards, how
many ways can the cards be drawn with exactly three club cards?
A. 286
B. 220
C. 8800
D. 11154
_____
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Probability
A. 1/6
B. 1/3
C. 2/3
D. 5/6
_____
82. A card is drawn at random from an ordinary deck of 52 playing cards.
Find the probability that it is an ace,
A. 1/52
B. 1/26
C. 1/13
D. 1/12
_____
83. A card is drawn at random from an ordinary deck of 52 playing cards.
Find the probability that it is a three of clubs or a six of diamonds.
A. 1/52
B. 1/26
C. 1/13
D. 1/12
_____
84. A ball is drawn at random from a box containing 6 red balls, 4 white
balls, and 5 blue balls. Determine the probability that it not red.
A. 1/5
B. 2/5
C. 3/5
D. 4/5
_____
85. Determine the probability of throwing a total of 8 in a single throw
with two dice, each of whose faces is number from 1 to 6.
C. 5/36
D. 7/36
A. 1/18
B. 1/9
_____
86. Roll a pair of dice. What is the probability that the sum of two numbers
is 11?
A. 1/36
B. 1/9
C. 1/18
D. 1/20
_____
87. In a throw of two dice, the probability of obtaining a total of 10 or 12
A. 1/6
B. 1/9
C. 1/12
D. 1/18
_____
88. Eleven books, consisting of 5 engineering books, 4 mathematics
books, and 2 chemistry books, are placed on a shelf at random. What
is the probability that the books of each kind are all together?
A. 1/1155
B. 2/1155
C. 3/1155
D. 4/1155
_____
89. Five red blocks and 4 white blocks are placed at random in a row.
What is the probability that the extreme blocks are both red?
C. 5/18
D. 7/18
A. 2/9
B. 1/6
_____
90. Nine tickets, numbered from 1 to 9, are in a box. If 2 tickets are drawn
at random, determine the probability that both are odd.
C. 5/18
D. 2/9
A. 3/18
B. 5/9
_____
91. From the previous number. Find the probability that one is odd, and
one is even.
A. 3/18
B. 5/9
C. 5/18
D. 2/9
_____
92. A bag contains 6 red, 4 white, and 8 blue balls. If 3 balls are drawn at
random, determine the probability that all 3 are red.
A. 7/204
B. 1/204
C. 5/204
D. 3/204
_____
93. A bag contains 6 red, 4 white, and 8 blue balls. If 3 balls are drawn at
random, determine the probability that 2 are white and 1 is red.
A. 1/68
B. 3/68
C. 5/68
D. 7/68
_____
94. Three cards are drawn from a pack of 52 cards. Determine the
probability that all are aces.
A. 1/5555
B. 1/5552
C. 1/5525
D. 1/5255
_____
95. Three cards are drawn from a pack of 52 cards. Determine the
probability that all are spades.
A. 3/850
B. 7/850
C. 9/850
D. 11/850
_____
96. Five cards are to be drawn from a deck of 52 playing cards. Find the
probability that all are red cards,
A. 0.01926 B. 0.02843 C. 0.06732 D. 0.02531
_____
97. Four cards are to be drawn from a deck of 52 playing cards. Find the
probability that there are exactly two clubs.
A. 0.12349 B. 0.21349 C. 0.23149 D. 0.21934
_____
98. A batch of electronic parts contains 16, which are within a power
tolerance and 4, which are not. If 3 electronic parts are selected at
random from the batch, compute the probability that all three are
within the power tolerance.
C. 28/57
D. 32/57
A. 21
B. 25/57
_____
99. Three cards are drawn from a pack of 52, each card being replaced
before the next one is drawn. Compute the probability that all are
aces.
D. 1/2197
A. 1/1297
B. 1/1279
C. 1/2179
_____
100. Find the probability of drawing a 7, then a face card (K, Q or J) from a
standard 52-card deck with replacement.
69. Referring to the experiment of tossing a coin twice, let A be the event
“at least one head occurs”. Which of the following gives the sample
space for the event A?
A. {HT}
B. {TH}
C. {TH, HT} D. {HT, TH, HH}
_____
70. An experiment consists of selecting three items from a box of several
items. The three items are classified defective (D) or non-defective
(N) as they are selected. Give the sample space for the event where it
has exactly one defective?
A. (NNN, NND, DNN)
C. (DDD, DNN, NDD)
B. (DNN, NDN, NND)
D. (NDD, DND, DDN)
_____
71. An experiment consists of selecting three items from a box of several
items. The three items are classified defective (D) or non-defective
(N) as they are selected. Give the sample space for event where it has
at least two defectives in three?
A. {NDD, DND, DDN}
C. {NDD, DND, DDN, DDD}
B. {DDN, DDD, NDD}
D. {DDD}
_____
72. An experiment consists of selecting three items from a box of several
items. The three items are classified defective (D) or non-defective
(N) as they are selected. Give the sample space for the event where it
has at most one defective?
A. {NNN, NND, DNN}
C. {DNN, NDN, NND, DDN, DND}
B. {DNN, NDN, NND}
D. {NNN, DNN, NDN, NND}
_____
73. An experiment consists of inspecting items from a production line
until a defective (D) is found. Give the sample space for this
experiment. What is the sample space of which exactly one item is
inspected?
A. {D}
B. {N}
C. { }
D. ∅
_____
74. An experiment consists of inspecting items from a production line
until a defective (D) is found. Give the sample space for this
experiment. Which outcomes are in the event of which at least two
items are inspected?
A. {ND, NND, NNND, NNNND}
B. {ND, DN}
C. {ND, NND, NNND, NNNND, …}
D. {D, ND}
_____
75. An experiment consists of inspecting items from a production line
until a defective (D) is found. Give the sample space for this
experiment. Which outcomes are in the event of which at most five
items are inspected?
A. {D, ND, NND, NNND, NNNND}
B. {DNNNN, NDNNN, NNDNN, NNNDN, NNNND}
C. {NNNND, NNNDD, NNDDD, NNDDD, DDDDD}
D. {NNNND}
_____
76. Suppose a lot consisting of 100 items contains 5 defectives. If one item
is randomly selected, the probability P(item is defective) is:
A. 0.05
B. 0.5
C. 0.005
D. 0.0005
_____
77. If a die is rolled 5 times, what is the probability of obtaining five 6s in
a row?
Ans.
(1/6)⁵
_____
78. A dart target board consists of a center circle having a radius of 2
inches a square section with dimension of 6 in x 6 in and the radius of
the biggest circle is 6 in. The three cross-sections have the same
center at 0. Assuming the dart is equally likely to hit any point inside
the target. Find the probability that a dart thrown at the circular
target will hit the area outside the square.
Ans.
0.682
_____
79. An employee of a large company, Toyota Motors Inc., is promoted to
management and will be transferred within 6 months. The employee
is told that there is a 33% probability of being transferred to Cebu and
a 50% probability of being transferred to Davao. What is the
probability that the employee will be transferred to Cebu or Davao?
Ans.
0.83
_____
80. In an unbiased coin toss, the probability of getting heads or tails is
exactly ½. A coin is tossed and one gets heads. If the coin is tossed
again, the probability of getting head again is:
A. ½
B. 0
C. ¼
D. ⅓
_____
81. A single die is tossed once. Find the probability of a 2 or 5 turning up.
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A. 0.0167
B. 0.0178
C. 0.0181
D. 0.0195
_____
101. The probability that a certain man will be alive 25 years hence is 3/7,
and the probability that his wife will be alive 25 years hence is 4/5.
Determine the probability that, 25 years hence, at least one of them
will be alive.
A. 3/35
B. 4/35
C. 31/35
D. 32/35
_____
102. A component fails a particular test (A) 15% of the time or a
component displays strain but does not fail the test (B) 25% of the
time.
(a) What is the probability that the component does not fail the test?
(b)
What is the probability that a component works
perfectly (neither displays strain nor fails the test)?
(c) What is the probability that the component either fails or shows
strain in the test?
Answers: (a) 0.85 (b) 0.6 (c) 0.4
_____
103. A box contains 58 red marbles, 14 yellow marbles, 28 blue marbles,
all the marbles are of the same size. Three marbles are drawn at
random from the box, first one, then a second, and then a third.
Determine the probability of getting one red marble, one yellow
marble, and one blue marble with replacement.
A. 0.0145
B. 0.0227
C. 0.0348
D. 0.0425
_____
104. A classroom contains 71 students. 10 of them are Chinese, 24 are
Japanese and 37 are Filipinos. If three students are randomly asked to
get out of the room, one after the other, what are the probabilities that
all 3 students are Chinese?
A. 0.00021 B. 0.00032 C. 0.0036
D. 0.0042
_____
105.A box contains 100 washers, 24 of which are brass, 36 copper, and the
remainder are steel. One washer is taken at random and retained, and
a second washer similarly drawn. Determine the probability that the
first is brass, and the second is copper.
A. 0.1296
B. 0.0873
C. 0.0864
D. 0.1936
_____
106. A box contains 74 brass washers, 86 steel washers, and 40 aluminum
washers. Three washers are drawn at random from the box with
replacement. Find the probability that there are no aluminum
washers drawn.
A. 0.4819
B. 0.5101
C. 0.5852
D. 0.6652
_____
107. Nine pingpong balls number are placed in tambulo. You randomly
draw two balls. What is the probability that the first number is odd
and the second number is even if there is a replacement for the first
ball before selecting the second?
A. 0.247
B. 0.274
C. 0.427
D. 0.472
_____
108. A quality engineer selects 3 iPods from a box that contains 20 iPods
of which 3 are defective. What is the probability that the first is
defective and the others are not defective?
A. 0.295
B. 0.204
C. 0.119
D. 0.122
_____
109. A box contains 5 defective and 195 non-defective cell phones. A
quality control engineer selects two cell phones at random without
replacement. What is the probability that neither is defective?
C. 0.00066 D. 0.00051
A. 0.95063 B. 0.9505
_____
110. A box contains 5 defective and 195 non-defective cell phones. A
quality control engineer selects two cell phones at random without
replacement. What is the probability that both are defective
A. 0.00050 B. 0.0007
C. 0.00053 D. 0.00063
_____
111. A box contains 5 defective and 195 non-defective cell phones. A
quality control engineer selects two cell phones at random with
replacement. What is the probability that neither is defective?
A. 0.950625 B. 0.9505
C. 0.00066 D. 0.00051
_____
112. A box contains 5 defective and 195 non-defective cell phones. A
quality control engineer selects two cell phones at random with
replacement. What is the probability that both are defective
A. 0.00050 B. 0.0007
C. 0.00053 D. 0.000625
_____
113. A box contains 5 defective and 195 non-defective cell phones. A
quality control engineer selects two cell phones at random without
replacement. What is the probability that exactly one is defective?
A. 0.0245
B. 0.0490
C. 0.0488
D. 0.0244
_____
Probability
114. A box contains 5 defective and 195 non-defective cell phones. A
quality control engineer selects two cell phones at random with
replacement. What is the probability that exactly one is defective?
C. 0.04875 D. 0.0244
A. 0.0245
B. 0.0490
_____
115. A man holds 2 of a total of 20 tickets in a lottery. If there are 2 winning
tickets, determine the probability that he has exactly one.
A. 9/95
B. 12/95
C. 15/95
D. 18/95
_____
116. There are three candidates, A, B, and C, for an office. The odds that A
will win are 7 to 5, and the odds that B will win are 1 to 3. (a) What is
the probability that either A or B will win?
B. 5/6
C. 6/48
D. 6/7
A. 7/48
_____
117. An urn contains 4 black balls and 6 white balls. What is the probability
of getting 1 black and 1 white ball in two consecutive draws from the
urn?
C. 0.53
D. 0.04
A. 0.24
B. 0.27
_____
118. One bag contains 4 white balls and 2 black balls; another bag contains
3 white balls and 5 black balls. If one ball is drawn from each bag,
determine the probability that 1 is white and 1 is black.
C. 13/24
D. 17/24
A. 7/24
B. 11/24
_____
119. From a bag containing 4 black balls and 5 white balls, two balls are
drawn one at a time. Find the probability that one ball is white and
one ball is black. Assume that the first ball is returned before the
second ball is drawn.
A. 16/81
B. 25/81
C. 20/81
D. 40/81
_____
120. One bag contains 5 white balls and 4 black balls and a second bag
contains 2 white and 4 black balls. One ball is drawn from the second
bag and is placed unseen in the first bag. What is the probability that
the ball now drawn from the first bag is white?
A. 5/21
B. 8/15
C. 23/63
D. 1/15
_____
121. One purse contains 5 dimes and 2 quarters, and a second purse
contains 1 dime and 3 quarters. If a coin is taken from one of the two
purses at random, what is the probability that it is a quarter?
A. 29/56
B. 29/65
C. 32/65
D. 23/56
_____
122. One purse contains 6 copper coins and 1 silver coin; a second purse
contains 4 copper coins. Five coins are drawn from the first purse and
put into the second, and then 2 coins are drawn from the second and
put into the first. Determine the probability that the silver coin is in
the second purse.
A. 1/9
B. 2/9
C. 4/9
D. 5/9
_____
123. From the previous problem. Determine the probability that the silver
coin is in the second purse.
C. 4/9
D. 5/9
A. 1/9
B. 2/9
_____
124. A box contains 7 tickets, numbered from 1 to 7 inclusive. If 3 tickets
are drawn from the box, one at a time, determine the probability that
they are alternately either odd, even, odd or even, odd, even.
A. 1/7
B. 2/7
C. 3/7
D. 4/7
_____
125. The probability that A can be solve a given problem is 4/5, that B can
solve it is 2/3, and that C can solve it is 3/7. If all three try, computer
the probability that the problem will be solved.
C. 101/105 D. 104/105
A. 92/105
B. 97/105
_____
126. What is the probability of getting at least 1 one in 2 throws of a die?
A. 11/36
B. 13/36
C. 23/36
D. 26/36
_____
127. The probability of A's winning a game of chess against B is 1/3. What
is the probability that A will win at least 1 of a total of 3 games?
A. 8/27
B. 11/27
C. 16/27
D. 19/27
_____
128. Find the probability that in tossing a fair coin three times, there will
appear at least 1 head.
A. 7/8
B. 2/3
C. 5/8
D. 1/3
_____
129. Find the probability that in a family of 4 children there will be at least
1 boy. Assume that the probability of a male birth is ½..
D. 15/16
A. 9/16
B. 11/16
C. 13/16
_____
130. Find the probability of getting a total of 7 at least once in three tosses
of a pair of fair dice.
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Probability
whole lot are perfect, what is the probability that the lot will be
accepted?
A. 0.581
B. 0.851
C. 0.729
D. 0.927
A. 91/126
B. 91/216
C. 95/126
D. 95/216
_____
131. If the probability that the average freshman will not complete four
years of college is 1/3, what is the probability p that of 4 freshmen at
least 3 will complete four years of college?
C. 16/27
D. 19/27
A. 8/27
B. 11/27
_____
132. The probability of getting exactly 2 heads in 6 tosses of a fair coin is
A. 11/64
B. 13/64
C. 15/64
D. 17/64
_____
133. Find the probability that in five tosses of a fair die, a 3 will appear
twice.
A. 625/3888 B. 265/3888 C. 345/3888 D. 435/3888
_____
134. Find the probability that in five tosses of a fair die, a 5 will appear at
most once,
A. 1235/3888 B. 1325/3888 C. 2135/3888 D. 3125/3888
_____
135. According to statistics 30% of smokers want to quit smoking. In a
random of 12 smokers, what is the probability that the number of who
want to quit smoking is exactly 6?
A. 0.0792
B. 0.0836
C. 0.0942
D. 0.0632
_____
136. Sixty percent of the employees of a certain company have at least one
credit card. If a random sample of 12 employees, what is the
probability that 5 of them have at least one credit card?
D. 0.1009
A. 0.9100
B. 0.1900
C. 0.1090
_____
137. If the probability that it will rain on any given day this week is 60%,
find the probability that it will rain exactly 3 out of 7 days this week.
A. 0.1359
B. 0.1593
C. 0.1935
D. 0.1953
_____
138. An automatic machine produces an average 10% of its components
outside of tolerance required. In a sample of 10 components from the
machine, determine the probability of having 3 components outside
of tolerance required.
B. 0.0574
C. 0.0745
D. 0.0754
A. 0.0475
_____
139. Calculate the probability of randomly guessing at least 7 correct
answers on a 10-question true or false quiz to get a passing a grade.
A. 0.127
B. 0.172
C. 0.712
D. 0.721
_____
140. A traffic control engineer reports that 75% of the vehicles passing
through a checkpoint are from within the city. What is the probability
that fewer than 4 of the next 9 vehicles are from out of the city?
D. 0.8343
A. 0.3483
B. 0.3834
C. 0.4833
_____
141. If 20% of the bolts produced by a machine are defective, determine
the probability that out of 4 bolts chosen at random, less than 2, bolts
will be defective.
C. 0.8192
D. 0.9821
A. 0.1892
B. 0.2981
_____
142. Teams A and B are playing in a league. They will pay each other 5
times. If the probability that A wins a game is ⅓, what is the
probability that team A will win at least three of the five games?
A. 0.12
B. 0.21
C. 0.34
D. 0.43
_____
143. It has been estimated that about 30% of frozen chicken contain
enough salmonella bacteria to cause illness if improperly cooked. A
consumer purchases 12 frozen chickens. What is the probability that
the consumer will have at least 6 contaminated chickens?
A. 0.1178
B. 0.1718
C. 0.1781
D. 0.1871
_____
144. A manufacturer has the following quality control check at the end of a
production line: If at least eight of ten randomly picked articles meet
all specifications, the whole shipment is approved. If, in reality, 85%
of a particular shipment meet all specifications, what is the
probability that the shipment will make it through the control check?
A. 0.280
B. 0.370
C. 0.820
D. 0.730
_____
145. A grocery store manager notes that 35% of customers who buy a
particular product make use of a store coupon to receive a discount.
If seven people purchase the product, what is the probability that
fewer than four will use a coupon?
A. 0.60
B. 0.70
C. 0.80
D. 0.90
_____
146. An inspection procedure at a manufacturing plant involves picking
three items at random and then accepting the whole lot if at least two
of the three items are in perfect condition. If in reality 90% of the
_____
147. A box contains 5 red balls, 4 white balls, and 3 blue balls. A ball is
selected at random from the box, its color is noted, and then the ball
is replaced. Find the probability that out of 6 balls selected in this
manner, 3 are red, 2 are white, and 1 is blue.
A. 325/5184 B. 425/5184 C. 725/5184 D. 625/5184
_____
148. A fair is thrown 5 times. On any one throw, outcome 1 is that an even
number appears, outcome 2 is that a 1 or 3 appears, and outcome 3 is
that a 5 appears. Find the probability that in the 5 throws, outcome 1
occurs twice, outcome 2 occurs twice, and outcome 3 occurs once.
A. 0.888143 B. 0.148838 C. 0.138848 D. 0.1888889
_____
149. If a fair die is to be tossed 12 times, the probability of getting 1, 2, 3, 4,
5 and 6 points exactly twice each is
A. 0.00344 B. 0.00434 C. 0.00334 D. 0.00343
_____
150. Based on past experience, the makeup of Dr. Stephens’ statistics for
engineers class has consisted of 20% civil engineers, 30% chemical
engineers, 40% industrial engineers, and 10% electrical engineers.
Given that these probabilities still hold, what is the probability that
her 2010 classes will consist of 25 civil engineers, 30 chemical
engineers, 40 industrial engineers, and 10 electrical engineers?
A. 0. 00047 B. 0.00074 C. 0.00036 D. 0.00063
_____
151. The probabilities that the light bulb of the projector used in Dr.
Stephen’s statistical engineering software course will last less than 40
hours, 40 to 80 hours, or more than 80 hours are 0.3, 0.5, and 0.2. Find
the probability that among 8 such bulbs, 2 will last less than 40 hours,
5 will last between 40 and 80 hours, and 1 will last more than 80
hours.
A. 0.0459
B. 0.0594
C. 0.0549
D. 0.0945
_____
152. A traffic engineer knows that at a certain intersection over a 24-hour
period, no accidents occur within probability 0.25, one accident
occurs with probability 0.60, and two or more accidents occur with
probability of 0.15. What is the probability that over ten 24-hour
periods, no accidents occur 3 times, one accident occurs 6 times and
two or more accidents occur once?
A. 0.01968 B. 0.25000 C. 0.01094 D. 0.09185
_____
153. A traffic engineer is studying accidents and finds that 15% are 1-car
accidents, 65% are 2-car accidents, 15% are 3-car accidents, and 5%
are 4-car accidents in the area he is studying. He randomly selects 10
accidents. Find the probability that in the 10 selected, 2 are 1-car
accidents, 5 are 2-car accidents, 2 are 3 car accidents, and 1 is 4-car
accidents.
B. 0.0222
C. 0.0333
D. 0.0444
A. 0.0111
_____
154. Items under inspection are subjected to two types of defects. About
70% of the items in a large lot are defect-free, 20% have a type A
defect, and 10% have a type B defect. Six of the items are randomly
selected. Find the probability that 3 have no defects, 1 has a type A
defect, and 2 have a type B defect.
A. 0.014
B. 0.023
C. 0.032
D. 0.041
_____
155. Suppose only 12% of men in ancient Greece were honest. What is the
probability that the first honest man he encounters will be no later
than the fourth man he meets?
B. 0.4003
C. 0.5006
D. 0.6005
A. 0.3004
_____
156. A box contains 6 blue marbles and 4 red marbles. An experiment is
performed in which a marble is chosen at random and its color
observed, but the marble is not replaced. Find the probability that
after 5 trials of the experiment, 3 blue marbles will have been chosen.
A. 5/21
B. 8/21
C. 10/21
D. 13/21
_____
157. A janitor with a bunch of 9 keys is to open a door but only one key can
open. What is the probability that he will succeed in 3 trials?
A. 0.375
B. 0.425
C. 0.333
D. 0.111
_____
158. Ten percent of the tools produced in a certain manufacturing process
turn out to be defective. Find the probability that in a sample of 10
tools chosen at random, exactly 2 will be defective, by using the
Poisson distribution.
A. 0.1398
B. 0.1839
C. 0.3198
D. 0.3918
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Probability
173. A trucking firm determines that its fleet of trucks averages a mean of
12.4 miles per gallon with a standard deviation of 1.2 miles per gallon
on cross-country hauls. What is the probability that one of the trucks
averages fewer than 10 miles per gallon?
A. 0.0228
B. 0.0339
C. 0.0446
D. 0.0552
_____
174. A factory dumps an average of 2.43 tons of pollutants into a river
every week. If the standard deviation is 0.88 tons, what is the
probability that in a week more than 3 tons are dumped?
A. 0.2578
B. 0.2875
C. 0.5287
D. 0.5827
_____
175. An electronic product takes an average of 3.4 hours to move through
an assembly line. If the standard deviation is 0.5 hour, what is the
probability that an item will take between 3 and 4 hours?
A. 0.37607 B. 0.67307 C. 0.70367 D. 0.77603
_____
176. The mean weight of 500 male students at a certain college is 151 lb
and the standard deviation is 15 lb. Assuming that the weights are
normally distributed, find how many students weigh between 120
and 155 lb
B. 300
C. 320
D. 340
A. 280
_____
177. The mean inside diameter of a sample of 200 washers produced by a
machine is 0.502 inches and the standard deviation is 0.005 inches.
The purpose for which these washers are intended allows a maximum
tolerance in the diameter of 0.496 to 0.508 inches, otherwise the
washers are considered defective. Determine the percentage of
defective washers produced by the machine, assuming the diameters
are normally distributed.
B. 23%
C. 25%
D. 28%
A. 21%
_____
178. A large batch of electric light bulbs has a mean time of failure of 2400
hours and a standard deviation of 320 hours. If a random sample of
40 light bulbs is drawn from the batch, determine the probability that
the mean time of failure will be less than 2300 hours.
A. 0.032
B. 0.015
C. 0.024
D. 0.047
_____
179. A large batch of electric light bulbs has a mean time of failure of 2400
hours and the standard deviation of 60 hours for a batch of 4200
bulbs. How many light bulbs will likely last more than 2500 hours?
A. 201
B. 256
C. 183
D. 154
_____
180. In normal random distribution, it is found out that the mean is 80 and
standard deviation is 5, which of the following ranges in which 84%
of the data lies?
B. 65 - 85
C. 70 - 90
D. 75 – 95
A. 60 - 80
_____
181. What is the standard deviation of the normal distribution that
approximates a binomial distribution consisting of 119 trials within
probability of 0.70 of success?
C. 5
D. 6
A. 3
B. 4
_____
182. Compute the standard deviation of the normal distribution that
approximates a binomial distribution. There are 60 trials with a
probability of failure of 0.25.
A. 2.45
B. 3.35
C. 4.25
D. 5.15
_____
183. Of the coral reef species on the Great Barrier Reef off Australia, 73%
are poisonous. If at mist boat taking divers to different points off the
reef encounters an average of 25 coral reef species, what are the mean
and standard deviation for he expected number of poisonous species
seen?
A. μx = 6.75, σx = 4.93
C. μx = 18.25, σx = 4.93
B. μx = 18.25, σx = 2.22
D. μx = 18.25, σx = 8.88
_____
184. A die is tossed 120 times. Find the probability that the face 4 will turn
up 18 times or less, assuming the die is fair.
A. 0.3557
B. 0.5337
C. 0.5773
D. 0.7553
_____
185. A fair coin is tossed 500 times. Find the probability that the number
of heads will not differ from 250 by more than 10.
A. 0.2586
B. 0.5268
C. 0.6528
D. 0.8265
_____
186. If 60% of the population support massive federal budget cuts, what is
the probability that in a survey of 250 people at most 155 people
support such cuts?
B. 0.7611
C. 0.7822
D. 0.8722
A. 0.6711
_____
_____
159. If the probability that an individual will suffer a bad reaction from
injection of a given serum is 0.001, determine the probability that out
of 2000 individuals exactly 3 individuals will suffer a bad reaction.
C. 0.180
D. 0.190
A. 0.160
B. 0.170
_____
160. From the previous problem, determine the probability that out of
2000 individuals more than 2 individuals will suffer a bad reaction.
A. 0.232
B. 0.323
C. 0.454
D. 0.545
_____
161. A manufacturer estimates that 0.25% of his output of a component
are defective. The components are marketed in packets of 200. Using
Poisson’s distribution, determine the probability of a packet
containing only 2 defective components.
B. 0.758
C. 0.0785
D. 0.0857
A. 0.578
_____
162. If 3% of the electric bulbs manufactured by a company are defective,
find the probability that in a sample of 100 bulbs, 4 bulbs will be
defective.
A. 0.168
B. 0.178
C. 0.718
D. 0.816
_____
163. From the previous problem, find the probability that in a sample of
100 bulbs, more than 5 bulbs will be defective.
A. 0.0398
B. 0.0839
C. 0.0893
D. 0.0983
_____
164. A manufacturer estimates that 1.5% of his output of a small item is
defective. Find the probabilities that in a pack of 200 items, three or
more are defective.
D. 0.577
A. 0.224
B. 0.423
C. 0.1494
_____
165. The number of cars entering the tool plaza on a bridge during the hour
after midnight follows a Poisson distribution with a mean of 20. What
is the probability that 17cars will pass through the toll plaza during
that hour on any given night.
A. 6.7%
B. 7.6%
C. 8.9%
D. 9.8%
_____
166. The number of road construction projects that take place at any one
time in a certain city follows a Poisson distribution with a mean of 3.
Find the probability that exactly five road construction projects are
currently taking place in this city.
A. 0.100532 B. 0.100819 C. 0.200521 D. 0.200829
_____
167. The number of road construction projects that take place at any one
time in a certain city follows a Poisson distribution with a mean of 7.
Find the probability that more than four road construction projects
are currently taking place in the city.
C. 0.827
D. 0.872
A. 0.728
B. 0.782
_____
168. Suppose the number of babies born during an 8-hour shift at a
hospital's maternity wing follows a Poisson distribution with a mean
of 6 an hour. Find the probability that five babies are born during a
particular 1-hour period in this maternity wing.
D. 0.1606
A. 0.1303
B. 0.1404
C. 0.1505
_____
169. The university policy department must write, on average, five tickets
per day to keep department revenues at budgeted levels. Suppose the
number of tickets written per day follows a Poisson distribution with
a mean of 8.8 tickets per day. Find the probability that less than six
tickets are written on a randomly selected day from this distribution.
B. 0.1284
C. 0.1428
D. 0.1482
A. 0.1248
_____
170. A lathe machine in a mechanical shop breaks down an average of 4
times per year. Using Poissons distribution, find the probability that
at most 1 breakdown will occur each year.
A. 0.1079
B. 0.1709
C. 0.1907
D. 0.1970
_____
171. Communications engineers have determined that lifetimes of Ace cell
phones are normally distributed with a mean equal to 60 months and
a standard deviation equal to 5 months. What is the probability that a
cellphone of this type has lifetime less than 55 months?
A. 0.29602 B. 0.84134 C. 0.34134 D. 0.15866
_____
172. The amount of time that a teenager plays videogames in any given
week is normally distributed. If a teenager plays videogames an
average of 15 hours per week with a standard deviation of 3 hours,
what is the probability of a teenager playing videogames between 9
and 21 hours?
B. 95.4%
C. 96.5%
D. 97.9%
A. 94.5%
_____
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187. Health official from DOH who have studied a particular virus say that
50% of all the Filipino people have had the virus. If a random of 144
people is taken, what is the probability that fewer than 60 had the
virus?
A. 0.023
B. 0.032
C. 0.045
D. 0.054
_____
188. Among 10,000 random digits, find the probability that the digits 3
appear at most 950 times.
A. 0.4467
B. 0.4647
C. 0.4746
D. 0.4764
_____
189. In 2017, about 1 in 43 births resulted in twins. If a barangay has 2150
births that year, find the probability that between 29 and 50 of them
were twins.
B. 0.4987
C. 0.7489
D. 0.7984
A. 0.4789
_____
190. One thousand copper rods have the properties shown in the table.
Diameter
Too thin
OK
Too thick
Length
Too short
10
5
5
OK
40
902
7
Too long
4
20
7
If the rod meets the length specifications, find the probability the rod
meets the diameter specifications.
B. 0.95
C. 0.96
D. 0.97
A. 0.94
_____
191. From the previous problem. If the meets the diameter specifications,
find the probability the rod meets the length specifications.
A. 0.94
B. 0.95
C. 0.96
D. 0.97
_____
192. On the East Coast, it is known from health records that the probability
of selecting an adult over 40 years of age with cancer is 0.05. The
probability of diagnosing a person with cancer as having the disease
is 0.78 and the probability of incorrectly diagnosing a person without
cancer as having the disease is 0.06. Find the probability that a person
is diagnosed as having cancer.
A. 0.0390
B. 0.0570
C. 0.0960
D. 0.0620
_____
193. From the previous problem. Find the probability that a person
diagnosed as having cancer actually has the disease?
A. 0.59375 B. 0.40625 C. 0.3690
D. 0.2755
_____
194. Suppose that, in a certain part of the world, any 50-year period the
probability of a major plague is .39, the probability of a major famine
is .52, and the probability of both a plague and a famine is .15. What is
the probability of a famine given that there is a plague?
A. .288
B. .385
C. .513
D. .760
_____
195. A process manufactures aluminum cans. The probability that a can
has a flaw on the side is 0.02, the probability that it has a flaw on the
top is 0.03, and the probability that it has a flaw on the top and the
side is 0.01. What is the probability that a can will have flaw on its
side, given that it has a flaw on the top?
A. 3/50
B. 1/25
C. 1/2
D. 1/3
_____
196. A box contains black chips and red chips. A person draws two chips
without replacement. If the probability of selecting a black chip and a
red chip is 15/56 and the probability of drawing a black chip on the
first draw is 3/4, what is the probability of drawing a red chip on the
second draw, if you know the first chip drawn was black?
A. 3/14
B. 5/14
C. 9/14
D. 11/14
_____
197. The probability that a student takes chemistry and is on the honor
rolls is 0.042. The probability that a student is on the honor roll is
0.21. What is the probability that the student is taking chemistry,
given that the student is on the honor roll?
B. 0.20
C. 0.30
D. 0.40
A. 0.10
_____
198. In a certain college, 5% of the men and 2% of the women took
engineering. Furthermore, 60% of the students are men. If a student
is selected at random, and is found to be an engineering student, what
is the probability that the student is a man?
A. 15/19
B. 3/10
C. 16/19
D. 4/13
_____
199. At the Pine Valley Country Club, 32% of the members play golf and
are female. Also, 80% of the members play golf. If a member of the
club is selected at random, find the probability that the member is
female give that the member plays golf.
D. 0.40
A. 0.10
B. 0.20
C. 0.30
_____
Probability
200. In a certain region of the country it is known from experience that the
probability of selecting an adult over 40 years of age with a cancer is
0.02. If the probability of a doctor correctly diagnosing a person with
a cancer as having the disease is 0.78 and the probability of
incorrectly diagnosing a person without cancer as having the disease
is 0.06, what is the probability that a person is diagnosed as having
cancer?
B. 7.44%
C. 10.34%
D. 22.88%
A. 16.28%
_____
201. A plant has three suppliers. S1 supplies 30% of the parts of the plant,
S2 supplies 50% of the parts, and S3 supplies the remaining 20%. One
percent of the parts supplied by S1 are defective, two percent of the
parts supplied by S2 are defective, and three parts supplied by S3 are
defective. Given that the part was defective, what is the probability
that it came from supplier S3?
A. 0.5263
B. 0.4737
C. 0.1579
D. 0.3158
_____
202. A Ford has engines in three sizes. Of the Ford cars sold, 50% have the
smallest engine, 40% have the medium engine. Of the cars with the
smallest engine, 15% fail an emissions test within two years of
purchase. The failure figure for medium size engines is 10%, and the
failure figure for the largest engines is 5%. What is the probability that
this Ford will fail the emissions test within two years?
A. 0.12
B. 0.20
C. 0.18
D. 0.22
_____
203. If the probability of a spacecraft being struck by exactly one cosmic
particle during and Earth-Neptune roundtrip is identical to its
probability of not being struck at all, what is this probability?
A. 0.368
B. 0.135
C. 0.513
D. 0.638
_____
204. On a university campus, 60%, 30%, and 10% of the computers use
Windows, Apple, and Linux operating systems, respectively. A new
virus affects 3% of the Windows, 2% of the Apple, and 1% of the Linux
operating systems. What is the probability a computer on this campus
has the virus?
A. 0.036
B. 0.025
C. 0.063
D. 0.052
_____
205. A chemical supply company ships a chemical in 5-gallon drums. X
represents the number of drums ordered by a randomly chosen
customer. X has the following distribution.
X
1
2
3
4
5
P(X)
.1
.1
.2
.2
.4
Find the mathematical expectation of X.
A. 3.2
B. 3.5
C. 3.7
D. 3.9
_____
206. The group of engineers decide to play the game of craps. A pair of dice
is rolled in this game and the sum to appear on the dice is of interest.
What is the mathematical expectation of the sum to appear when the
dice are rolled?
C. 7
D. 8
A. 5
B. 6
_____
207. How many people would you expect to meet before you met one who
was born on a Wednesday?
A. 6
B. 7
C. 10
D. 14
_____
208. The number of defective welds in a length of pipe 0 through 6 with the
following probabilities.
X
0
1
2
3
4
5
6
P(X) 0.60 0.30 0.05 0.02 0.01 0.01 0.01
Find the expected value of the number of defective welds.
D. 0.61
A. 0.52
B. 0.55
C. 0.59
_____
209. The probability that a relay remains open is 0.5. An electrical circuit
consist of three such relays. The number of relays that remain open in
three are 0, 1, 2, or 3. The number of relays that remain open is
represented by X. The number of relays that remain open has the
following values with the probabilities.
X
0
1
2
3
P(X)
0.125
0.375
0.375
0.125
Find the expected value of the number of open relays.
A. 1.00
B. 1.25
C. 1.50
D. 1.75
_____
210. A game is played as follows. You pay $1 to play. A coin is flipped four
times. If four tails or four heads are obtained, you get your 1$ back
plus $5 more. Otherwise you forfeit your $1. What it the mathematical
expectation?
A. 0.25
B. 0.75
C. -0.25
D. 0.50
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Gillesania Engineering Review and Training Center ‐ 2022
Probability
_____
212. Assuming that each packet of cigarettes from a certain manufacturer
contains, as a premium, one of a set of 52 playing cards, and that these
cars are distributed among the packets at random (the number of
packets available being infinite), what is the average minimum
number of packets that must be purchased in order to obtain a
complete set of cards?
A. 236
B. 263
C. 326
D. 36
_____
211. An engineering company prepares an estimate for a job. The cost of
preparing the estimate is P10,000. The amount of profit over and
above the P10,000 is P25,000, if their estimate is accepted. The
probability that their estimate will be accepted is 0.70 and the
probability that their estimate will not be accepted is 0.30. What is the
expected profit?
A. P 14,500 B. P 15,200 C. P 15,800 D. P 16,500
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