Introduction to Business Statistics I (QM - 120)
Review problems for chapter 4
Problem # 1
True/False
1.
Probability of an uncertain outcome is a number between -1 and +1; if it is -1, the outcome will never occur and if it is +1, it will certainly occur.
2.
The three general methods of assigning probabilities are: the classical method, the relative frequency method, and the subjective method.
3.
Events that cannot be decomposed into other events are called elementary events.
4.
The sample space for an experiment, which involves rolling a pair of 6-faced dice, contains 6 elementary events.
5.
If two events are mutually exclusive, they cannot be statistically independent.
6.
The probability of the union of two events is always equal to the sum of the marginal probabilities of two events.
7.
If two events are independent, the joint probability of the two events is always equal to the product of the marginal probabilities of two events.
8.
If the conditional probability of an event A given another event B is same as the marginal probability of the event A, then events A and B are mutually exclusive.
9.
If the joint probability of neither of two events, A and B, occurring is 0.08, the probability of either A or B occurring is 0.92.
10.
Assigning probabilities by dividing the number of ways that an event can occur by the total number of possible outcomes in an experiment is called the relative frequency of occurrence method.
11.
If the occurrence of one event precludes the occurrence of another event, then the two events are independent.
12.
Given two events, A and B, if the probability of either A or B occurring is 0.8, then the probability of neither A nor B occurring is -0.8.
13.
An experiment is a process that produces outcomes.
1 Introduction to Business Statistics I (QM - 120) | M. Zainal

Problem # 2
Multiple Choices
1.
An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased. Based on the following joint probability table that was developed from the dealer's records for the previous year, P (Male) =
________.
Type of Buyer Gender
Vehicle Female Male Total
SUV
Not SUV
Total
.32
.40
.48
1.00 a) 0.48 b) 0.50 c) 0.20 d) 0.02 e) 0.60
2.
A complete listing or roster of all elementary events for an experiment is called
_____. a) an experiment b) a sample space c) a register d) a database e) a file
3. If X = {1, 3, 6, 7, 8, 9, 11, 15} and Y = {3, 4, 5, 6, 7, 9, 12}, then X U Y is ________. a) {1, 3, 5, 6, 7, 8, 9, 10, 12, 14, 15} b) {1, 3, 5, 6, 7, 9, 11, 12, 14, 15} c) {1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15} d) {1, 3, 5, 6, 7, 9, 11, 12, 13, 15} e) {1, 3, 5, 6, 8, 9, 11, 12, 13, 15}
2 Introduction to Business Statistics I (QM - 120) | M. Zainal

4.
If X = {1, 3, 6, 7, 8, 9, 11, 15} and Y = {3, 4, 5, 6, 7, 9, 12}, then X ∩ Y is ________. a) {1, 3, 5, 9} b) {3, 5, 7, 9} c) {3, 4, 7, 9} d) {3, 6, 7, 9} e) {1, 3, 6, 7}
5. If the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of another event, the two events are ________________________. a) collectively exhaustive b) non interacting c) mutually exclusive d) independent e) complementary
6. Sixty percent of all technical assistants would like to have a PC. Fifty percent of all technical assistants would like to have MAC. Twenty percent of all technical assistants would like to have both. If a technical assistant is randomly selected, what is the probability that she would like to have a PC or a MAC? a) 0.33 b) 1.00 c) 1.10 d) 0.90 e) 0.95
7. Consider the following 3x4 contingency table in which a sample of 1400 companies is summarized in terms of the company’s industry type (X, Y, or Z) and geographic location
(A, B, C, or D).
A B C D
X 124 110 108 114
Y 130 106 122 112
Z 128 118 112 116
What is the probability P(B │ Y)? a) 0.0757 b) 0.3174 c) 0.2255 d) 0.4985 e) 0.2485
3 Introduction to Business Statistics I (QM - 120) | M. Zainal

8. Sixty percent of all technical assistants would like to have a PC. Fifty percent of all technical assistants would like to have MAC. Twenty percent of all technical assistants would like to have both. If a technical assistant is randomly selected, what is the probability that she would like to have MAC, given that she would like to have a PC as well? a) 0.33 b) 0.60 c) 1.10 d) 0.90 e) 0.99
9. Consider the following 3x4 contingency table in which a sample of 1400 companies is summarized in terms of the company’s industry type (X, Y, or Z) and geographic location
(A, B, C, or D).
A B C D
X 124 110 108 114
Y 130 106 122 112
Z 128 118 112 116
What is the probability P(B ∩ Y)? a) 0.0757 b) 0.3174 c) 0.2255 d) 0.4985 e) 0.0957
10. If the occurrence of one event precludes the occurrence of another other event, then the two events are __________________. a) collectively exhaustive b) non interacting c) mutually exclusive d) independent e) joint events
4 Introduction to Business Statistics I (QM - 120) | M. Zainal

11. Consider the following 3x4 contingency table in which a sample of 1400 companies is summarized in terms of the company’s industry type (X, Y, or Z) and geographic location (A, B, C, or D).
A B C D
X 124 110 108 114
Y 130 106 122 112
Z 128 118 112 116
What is the probability P(B U Y)? a) 0.0757 b) 0.3174 c) 0.2255 d) 0.4986 e) 0.0985
12. An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased. Based on the joint probability table below that was developed from the dealer's records for the previous year, P (Female  SUV) =
_______.
Type of Buyer Gender
Vehicle Female Male Total
SUV
Not SUV
Total
.30 .40
.60 1.00 a) 0.30 b) 0.40 c) 0.12 d) 0.10 e) 0.60
13.
Given P(A) = 0.40, P(B) = 0.50, P(A  B) = 0.15. Find P(A  B). a) 0.90 b) 1.05 c) 0.75 d) 0.65 e) 0.60
5 Introduction to Business Statistics I (QM - 120) | M. Zainal

14.
Given P (A) = 0.40, P (B) = 0.50, P (A  B) = 0.15. Find P (A|B). a) 0.20 b) 0.80 c) 0.30 d) 0.375 e) 0.15
15.
Let A be the event that a student is enrolled in an accounting course, and let
S be the event that a student is enrolled in a statistics course. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting. A student is randomly selected, what is the probability that the student is enrolled in either accounting or statistics or both? a) 0.15 b) 0.85 c) 0.70 d) 0.55 e) 0.90
16.
Consider the following sample space, S, and several events defined on it. S =
{Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty,
Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. The complement of F is ___________. a) {Albert, Betty, Jack, Patty} b) {Betty, Patty, Meagan} c) {Albert, Abel, Jack} d) {Betty, Abel} e) {Meagan}
6 Introduction to Business Statistics I (QM - 120) | M. Zainal

Problem # 3
A college student is planning his weekend (i.e., Thursday night and
Friday night) activities. On Thursday night, he can sleep (30% chance), go to a movie theater (50% chance), or read. On Friday night, he can visit his family (80% chance) or do his homework. a.
Construct a tree diagram that would present the sequence of all possible weekend activities. b.
What is the probability that he will ultimately be doing his homework?
7 Introduction to Business Statistics I (QM - 120) | M. Zainal

Problem # 4
The probability that an employee selected at random from a work force at a certain factory is a male is 0.65; the probability that the employee is married is
0.75; and the probability that the employee is both married and male is 0.50. If an employee is selected at random, calculate the probability that the employee is: a.
Female d.
Female or married b.
Single c.
Single and female e.
Married given she is a female
8 Introduction to Business Statistics I (QM - 120) | M. Zainal

Problem # 4
A poll taken among 50 employees of an industrial firm on the question of changing the work week from five days (8 A.M.-5 P.M.) to four days (7 A.M.-6
P.M.) yielded the following results:
Classification of employees
Response Executive Sales person Office worker Plant worker Total
Favor change
Oppose change
No opinion
Totals
2
1
0
3
8
3
2
13
10
3
2
15
10
8
1
19
30
15
5
50
One employee is selected at random from among the 50. a.
What is the probability that an employee is a plant worker and favors the change? b.
What is the probability that the employee will oppose the change given that he is a salesperson? c.
If the employee is either an executive or a salesperson, what is the probability that he expressed no opinion? d.
Given that the employee is not a plant worker, what is the probability that he favors the change? e.
What is the probability that the employee either favors the change or is an office worker?
9 Introduction to Business Statistics I (QM - 120) | M. Zainal