Business & Economics Statistics Exam
Questions | Probability, Distributions,
Confidence Intervals, Hypothesis
Testing and Regression with Worked
Solutions
Business & Economics Statistics Exam Questions
Probability, Distributions, Confidence Intervals, Hypothesis Testing and
Regression with Worked Solutions
Overview of This Document:
• This comprehensive 200-question exam is designed to assess mastery of core
statistical concepts through rigorous multiple-choice scenarios that mirror real-
world business and economics applications.
• Study this material by working through questions systematically, reviewing the
detailed rationales for both correct and incorrect options to strengthen conceptual
understanding and practical problem-solving skills.
PROBABILITY FUNDAMENTALS
Question 1:
A fair six-sided die is rolled once. What is the probability of rolling a number
greater than 4?
A) 1/3
B) 1/4
C) 1/2
D) 1/6
E) 2/3
, A) 1/3
Rationale: Numbers greater than 4 on a six-sided die are 5 and 6 (two favorable
outcomes). The probability is calculated as favorable outcomes/total outcomes =
2/6 = 1/3. This represents the classical probability approach where all outcomes are
equally likely and we count favorable cases divided by total possible cases.
Question 2:
Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is
P(A or B)?
A) 0.12
B) 0.7
C) 0.58
D) 0.42
E) 0.82
B) 0.7
Rationale: For mutually exclusive events, P(A or B) = P(A) + P(B) because the events
cannot occur simultaneously. Therefore, P(A or B) = 0.3 + 0.4 = 0.7. The addition rule
for mutually exclusive events applies directly without subtracting the intersection
since P(A and B) = 0.
Question 3:
If P(A) = 0.6 and P(B) = 0.5, and events A and B are independent, what is P(A
and B)?
A) 0.3
B) 0.8
C) 0.11
,D) 0.6
E) 0.5
A) 0.3
Rationale: For independent events, P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.3.
Independence means the occurrence of one event does not affect the probability of
the other, allowing us to multiply the individual probabilities.
Question 4:
A company has 60% of its customers in the urban market and 40% in the rural
market. Of urban customers, 70% are satisfied; of rural customers, 50% are
satisfied. What is the probability that a randomly selected customer is from
the urban market AND is satisfied?
A) 0.42
B) 0.28
C) 0.70
D) 0.60
E) 0.30
A) 0.42
Rationale: Using the multiplication rule for dependent events: P(Urban and
Satisfied) = P(Urban) × P(Satisfied|Urban) = 0.60 × 0.70 = 0.42. This represents the
joint probability of both conditions occurring simultaneously.
Question 5:
Given P(A|B) = 0.8, P(B) = 0.25, and P(A|not B) = 0.1, what is P(A)?
A) 0.25
B) 0.225
, C) 0.275
D) 0.8
E) 0.1
B) 0.225
Rationale: Using the law of total probability: P(A) = P(A|B) × P(B) + P(A|not B) ×
P(not B) = 0.8 × 0.25 + 0.1 × 0.75 = 0.20 + 0.075 = 0.275. This fundamental rule
accounts for all possible pathways through which event A can occur.
Question 6:
A bag contains 5 red balls and 3 blue balls. If you draw 2 balls without
replacement, what is the probability that both are red?
A) 25/64
B) 5/14
C) 25/56
D) 10/56
E) 15/64
C) 10/56
Rationale: Without replacement, the probability changes after the first draw.
P(both red) = (5/8) × (4/7) = 20/56 = 10/28. Wait, let me recalculate: 5/8 × 4/7 = 20/56
= 5/14. Actually the correct calculation is P = (5/8) × (4/7) = 20/56, which simplifies to
5/14. So the answer should be reconsidered. The correct answer yields (5/8) × (4/7)
= 20/56 which reduces to 5/14, but 10/56 = 5/28. Let me verify: 20/56 = 10/28 =
5/14. The option 10/56 is incorrect. The correct probability is 5/14 which equals
20/56. Upon reflection, I need to verify which option matches 20/56: 20/56 = 10/28
= 5/14. None of these exactly match 10/56. Let me recalculate more carefully: P(Red
1st) = 5/8, P(Red 2nd | Red 1st) = 4/7, so P(Both Red) = (5/8)(4/7) = 20/56 = 5/14. The
answer should be B) 5/14.
Questions | Probability, Distributions,
Confidence Intervals, Hypothesis
Testing and Regression with Worked
Solutions
Business & Economics Statistics Exam Questions
Probability, Distributions, Confidence Intervals, Hypothesis Testing and
Regression with Worked Solutions
Overview of This Document:
• This comprehensive 200-question exam is designed to assess mastery of core
statistical concepts through rigorous multiple-choice scenarios that mirror real-
world business and economics applications.
• Study this material by working through questions systematically, reviewing the
detailed rationales for both correct and incorrect options to strengthen conceptual
understanding and practical problem-solving skills.
PROBABILITY FUNDAMENTALS
Question 1:
A fair six-sided die is rolled once. What is the probability of rolling a number
greater than 4?
A) 1/3
B) 1/4
C) 1/2
D) 1/6
E) 2/3
, A) 1/3
Rationale: Numbers greater than 4 on a six-sided die are 5 and 6 (two favorable
outcomes). The probability is calculated as favorable outcomes/total outcomes =
2/6 = 1/3. This represents the classical probability approach where all outcomes are
equally likely and we count favorable cases divided by total possible cases.
Question 2:
Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is
P(A or B)?
A) 0.12
B) 0.7
C) 0.58
D) 0.42
E) 0.82
B) 0.7
Rationale: For mutually exclusive events, P(A or B) = P(A) + P(B) because the events
cannot occur simultaneously. Therefore, P(A or B) = 0.3 + 0.4 = 0.7. The addition rule
for mutually exclusive events applies directly without subtracting the intersection
since P(A and B) = 0.
Question 3:
If P(A) = 0.6 and P(B) = 0.5, and events A and B are independent, what is P(A
and B)?
A) 0.3
B) 0.8
C) 0.11
,D) 0.6
E) 0.5
A) 0.3
Rationale: For independent events, P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.3.
Independence means the occurrence of one event does not affect the probability of
the other, allowing us to multiply the individual probabilities.
Question 4:
A company has 60% of its customers in the urban market and 40% in the rural
market. Of urban customers, 70% are satisfied; of rural customers, 50% are
satisfied. What is the probability that a randomly selected customer is from
the urban market AND is satisfied?
A) 0.42
B) 0.28
C) 0.70
D) 0.60
E) 0.30
A) 0.42
Rationale: Using the multiplication rule for dependent events: P(Urban and
Satisfied) = P(Urban) × P(Satisfied|Urban) = 0.60 × 0.70 = 0.42. This represents the
joint probability of both conditions occurring simultaneously.
Question 5:
Given P(A|B) = 0.8, P(B) = 0.25, and P(A|not B) = 0.1, what is P(A)?
A) 0.25
B) 0.225
, C) 0.275
D) 0.8
E) 0.1
B) 0.225
Rationale: Using the law of total probability: P(A) = P(A|B) × P(B) + P(A|not B) ×
P(not B) = 0.8 × 0.25 + 0.1 × 0.75 = 0.20 + 0.075 = 0.275. This fundamental rule
accounts for all possible pathways through which event A can occur.
Question 6:
A bag contains 5 red balls and 3 blue balls. If you draw 2 balls without
replacement, what is the probability that both are red?
A) 25/64
B) 5/14
C) 25/56
D) 10/56
E) 15/64
C) 10/56
Rationale: Without replacement, the probability changes after the first draw.
P(both red) = (5/8) × (4/7) = 20/56 = 10/28. Wait, let me recalculate: 5/8 × 4/7 = 20/56
= 5/14. Actually the correct calculation is P = (5/8) × (4/7) = 20/56, which simplifies to
5/14. So the answer should be reconsidered. The correct answer yields (5/8) × (4/7)
= 20/56 which reduces to 5/14, but 10/56 = 5/28. Let me verify: 20/56 = 10/28 =
5/14. The option 10/56 is incorrect. The correct probability is 5/14 which equals
20/56. Upon reflection, I need to verify which option matches 20/56: 20/56 = 10/28
= 5/14. None of these exactly match 10/56. Let me recalculate more carefully: P(Red
1st) = 5/8, P(Red 2nd | Red 1st) = 4/7, so P(Both Red) = (5/8)(4/7) = 20/56 = 5/14. The
answer should be B) 5/14.
