DESCRIPTIVE STATISTICS

1. What is the mean of the following data set? 14, 14, 15, 16, 28, 28, 32,
35, 37, 38.
A. 35.6 C. 33.4
B. 41.7 D. 25.7
2. What is the median of the following data set? 6, 12, 22, 18, 16, 4, 20,
5, 15.

A. 18.0 C. 16.0
B. 19.0 D. 15.0

3. Two thirds of people in a party are lawyers, whose average 1.Q. is 120.
The rest are engineers whose I.Q. is 180. What is the average 1.Q. of
all persons in the room?

A. 250 C. 140
B. 240 D. 150

4. 4. A set has 5 items and it has a range of 7. The set is composed of the
following: (1, 2, M, 5, M²) with M > 0. Find the average of the number
set.

A. 9.18 C. 13.22
B. 3.76 D. 5.11

5. Nicole earned a P2, 000 commission on a big deal, raising her average
commission by P100. Nicole's new average commission now is P900.
How many sales has she made so far?

A. 12 C. 14
B. 13 D. 15

6. A sample was taken of the ages in years of 12 people who attend a

movie. The results are as follows: 12 years, 10 years, 16 years, 22
years, 24 years, 18 years, 30 years, 32 years, 19 years, 20 years, 35
years, & 26 years. To the nearest year, what is the standard deviation
for this sample?

A. 10 yrs C. 8 yrs
B. 9 yrs D. 7 yrs

7. Calculate the sample variance for the following measurements of

weights of apple: 7 oz, 6 oz, 5 oz, 6 oz, & 9 oz.

A. 2.3 B. 1.3
 C. 0.3 D. 3.3

COUNTING PRINCIPLES

8. Without repeating any digit, how many 3-digit numbers can be made
out of the digits 5, 7, 2, 1, and 8?

A. 40 C. 60
B. 50 D. 120

9. 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 C. 15
B. 10 D. 45

10. The seven-digit telephone number of a certain town starts with

350. If the last four digits cannot begin or end with zero, how many
telephone numbers can be assigned?

A. 7290 C. 6561
B. 10000 D. 8100

11. The captain of a chess team assigns himself to board 1. If there

are six players (including the captain), how many ways can the team
be assigned to the boards if there are six chess boards.

A. 720 C. 240
B. 120 D. 60

Situation 1 - Without repeating any digit, how many 3-digit numbers can
you make out from numbers 0, 1, 3, 4, 8, 9 that are:

12. ① Greater than 480.

A. 47 C. 120
B. 52 D. 80

13. ② Less than 830.

A. 74 C. 64
B. 84 D. 120

14. ③ Greater than 300.

A. 100 B. 74
 C. 120 D. 64

Situation 2 - Six boys and four girls are to be seated on a bench. How many
ways can they be seated:

15. ① In any order?

A. 86400 C. 5234568
B. 120960 D. 3628800

16. ② If the girls must be seated next to each other?

A. 120960 C. 86400
B. 34560 D. 94350
17. ③ If the boys must be seated next to each other?
A. 34560 C. 94350
B. 86400 D. 120960

18. ④ If the boys must be seated side-by-side, and also the girls?

A. 120960 C. 34560
B. 86400 D. 94350

Situation 3 - How many ways can 6 persons line-up;

19. ① In any order?

A. 120 C. 480
B. 720 D. 640

20. ② If one person insist to stand in front?

A. 140 C. 100
B. 120 D. 80

21. If two of those persons refuses to stand next to each other?

A. 480 C. 360
B. 520 D. 440

22. A group of musicians is composed of three drummers, four

pianists, and five guitarists. How many ways can a trio are formed with
1 pianist, 1 drummer, and 1 guitarist?

A. 60 ways C. 40 ways
B. 90 ways D. 120 ways
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?

A. 792 C. 665280
B. 95040 D. 845
24. How many ways can 6 representatives are selected from a class
of 24 students?
A. 96909120 C. 246892
B. 78456924 D. 134596
25. How many line segments can be drawn (by connecting any two
points) from 9 distinct points?
A. 32 C. 36
B. 38 D. 40
26. How many ways can you invite any three of your eight friends to
come in your birthday party?
A. 72 C. 52
B. 64 D. 56
27. How many ways can you invite any one or more of your eight
friends to come in your birthday party?
A. 255 C. 128
B. 243 D. 356
28. A class contains 5 freshmen, 4 sophomores, 8 juniors and 3
seniors. A student is chosen at random to represent the class. Find the
probability that the student is
A. a sophomore C. a junior or senior
B. a senior
29. One card is selected at random from 50 cards numbered 1 to 50.
Find the probability that the number on the card is

A. divisible by 5 C. ends in the digit 2

B. prime

30. Of 10 girls in a class, 3 have blue eyes. If two of the girls are
chosen at random, what is the probability that

A. both have blue eyes? C. at least one has blue

B. neither has blue eyes? eyes?

31. Three bolts and three nuts are put in a box. If two parts are
chosen at random, find the probability that one is a bolt and one a nut.
 32. Ten students, A, B,..., are in a class. If a committee of 3 is chosen
at random from the class, find the probability that

A. A belongs to the C. A and B belongs to the

committee committee
B. B belongs to the D. A or B belongs to the
committee committee

33. A class consists of 6 girls and 10 boys. If a committee of 3 is

chosen at random from the class, find the probability that

A. 3 boys are selected C. at least one boy is

B. exactly 2 boys are selected
selected D. exactly 2 girls are selected

34. A pair of fair dice is tossed. Find the probability that the
maximum of the two numbers is greater than 4.
35. Of 120 students, 60 are studying French, 60 are studying
Spanish, and 20 are studying French and Spanish. If a student is
chosen at random, find the probability that the student
A. is studying French or Spanish
B. is studying neither French or Spanish
36. Three boys and 3 girls sit in a row. Find the probability that
A. the 3 girls sit together
B. the boys and girls sit in alternate seats
37. A point is selected at random inside an equilateral triangle whose
side length is 3. Find the probability that its distance to any corner is
greater than 1.

Situation 4 - In a random draw of five cards from a deck of 52 playing

cards, how many ways can the following be drawn:

38. ① Five red cards?

A. 32890 C. 1287
B. 2598960 D. 65780

39. ② Three Kings?

A. 69184 C. 4704
B. 5304 D. 4512

40. ③ Three Aces and a Queen?

 A. 768 C. 16
B. 704 D. 24

41. ④ Three Aces and 2 Kings?

A. 24 C. 16
B. 18 D. 12

PROBABILITY

42. From experience, a stockbroker believes that under present

economic conditions a customer will invest in tax - free bonds with a
probability of 0.60, will invest in mutual funds with a probability of
0.30, and will invest in both tax - free bonds and mutual funds with a
probability of 0.15. Now, find the probability that a customer will invest
in either tax - free bonds or mutual funds.
43. If each coded item in a catalogue begins with 3 distinct letters
followed by 4 distinct non zero digits, find the probability of randomly
selecting one of these coded items with the first letter a vowel and the
last digit even.
44. If a letter is chosen at random from the English alphabet, find
the probability that the letter is listed somewhere ahead of the letter j.
45. A pair of fair dice is tossed. Find the probability of getting at most
a total of 5.
46. If 3 books are picked at random from a shelf containing 5 novels,
3 books of poems, and a dictionary, what is the probability that the
dictionary is selected?
47. In a high school graduating class of 100 students, 54 studied
mathematics, 69 studied history, and 35 studied both mathematics
and history. If one of these students is selected at random, find the
probability that the student took mathematics or history.
48. Interest centers on life of an electronic component. Suppose it is
known that the probability that the component survives for more than
6000 hours is 0.42. Suppose also that the probability that the
component survives no longer than 4000 hours is 0.04. What is the
probability that the life of component is less than or equal to 6000
hours?
49. Interest centers on the nature of an oven purchased at a
department store. It can be either a gas or an electric oven. Consider
the decisions made by six distinct customers. Suppose that the
 probability is 0.40 that at most two of these individuals purchase an
electric oven. What is the probability that at least three purchase the
electric oven?
50. A box contains 10 black marbles, 8 red marbles, 8 white marbles,
and 2 yellow marbles. Suppose you can pull out a black marble from
the box and do not put it back. If you are to pull another marble, what
is the probability that you will pull out another black marble?
51. A classroom contains 71 students. 10 of them are Chinese, 24
are Japanese and 37 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 Japanese?
52. The probability that a construction generator will operate
satisfactorily for 5 years is 0.80 and that a welding machine will
operate satisfactorily over the same period is 0.75. Find the
probabilities that in a 5-year period both generators and welding
machine operate satisfactorily.
53. A dart target consists of three concentric circles with different
radii 1, 3, and 5 units. If a dart thrower always hits the area of a 5-unit
radius but hit the area randomly, what is the probability that a dart hits
the area of between the 1-unit radius circle and the 3 unit radius
circle?
54. A box contains 15 billiards balls, which are numbered 1 to 15. A
ball is drawn at random and the number is written down. Determine
the following probabilities that number is less than 5.
55. To win a lottery, a player must correctly select 6 different
numbers from 1 to 42. How many tickets would a person have to buy
to have a 1% chance of winning?
56. You have an equally likely chance of choosing any integer from 1
to 20. Find the probability of the given event a multiple of 3 is chosen.
57. Determine the probability of selecting at random a man from a
crowd containing 25 men and 15 women.

A. 0.714 C. 0.375
B. 0.833 D. 0.625

58. If a letter is chosen at random from the English alphabet, find the
probability that the letter follows the letter g.

A. 21/26 C. 10/13
B. 19/26 D. 9/1
 59. A dart is randomly thrown at a circular dartboard with target
circles having radii of 1, 3, and 5. Find the probability that the dart
lands on the shaded circular region between 1 and 3. Assume that the
dart will fall only within the 5 in radius.

A. 9/25 C. 2/5
B. 8/25 D. 3/5

60. Two six-sided dice are tossed. What is the probability that the
total of the two dice is 7 or 8?

A. 11/36 C. 5/36
B. 5/6 D. 1/6

Situation 5 - Five cards are to be drawn from a deck of 52 playing cards. Find
the probability that:

61. All are red cards,

A. 0.01926 C. 0.06732
B. 0.02843 D. 0.02531

62. Two are red and three are black,

A. 0.3765 C. 0.3251
B. 0.4267 D. 0.2853

63. There are three aces.

A. 0.001736 C. 0.001234
B. 0.002317 D. 0.003621

64. There are 3 queens but 4 are black.

A. 0.0002124 C. 0.0002501
B. 0.0004724 D. 0.0003892

Situation 6 - Three out of ten girls have blue eyes. If two girls are to be
chosen randomly, find the probability that:

65. The two girls have blue eyes.

A. 1/5 C. 3/100
B. 3/50 D. 1/15

66. Only one of them has blue eyes.

A. 2/50 B. 7/30
 C. 7/15 D. 3/100

67. Either one or both have blue eyes.

A. 7/10 C. 8/15
B. 23/30 D. 3/10

Situation 7 - The probability of event A happening is 3/5 and the probability

of event B happening is 2/3.

68. What is the probability of both A and B happening.

A. 3/5 C. 2/5
B. 1/5 D. 4/5

69. What is the probability of only event A happening, i.e. event A

happening and event B not happening.

A. 4/5 C. 3/5
B. 1/5 D. 2/5

70. What is the probability of either A, or B, or A and B happening.

A. 11/15 C. 3/5
B. 14/15 D. 13/15

71. A password of a computer used five digits where they are from 0
and 9. What is the probability that the password solely consists of
prime numbers and zero?

A. 1/32 C. 1/8
B. 1/16 D. ½

72. Consider 10 throws of an ordinary coin, the probability for heads

or tails equal to ½. What is the probability that exactly five heads will
turn up?

A. 0.246 C. 0.605
B. 0.524 D. 1.000

73. 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

74. If a jury of 12 people is to be selected randomly from a pool of 15

potential jurors, and the jury pool consists of 2/3 men and 1/3 women,
what is the probability that the jury will comprise at least 2/3 men?

A. 84/91 C. 5/91
B. 67/91 D. 24/91

75. Box A has 4 white balls, 3 blue balls, and 3 orange balls. Box B
has 2 white balls, 4 blue balls, and 4 orange balls. If one ball is drawn
from each box, what is the probability that one of the two balls will be
blue?

A. 0.52 C. 0.18
B. 0.28 D. 0.46

76. 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 C. 23/63
B. 8/15 D. 1/15

Situation 8 - 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:

77. Both washers are steel

A. 0.1480 C. 0.1576
B. 0.1600 D. 0.8000

78. The first is brass, and the second is copper.

A. 0.1296 C. 0.0864
B. 0.0873 D. 0.1936