,MATH 110 Module 3 | Practice Q&A | 2026/2027 | Statistics | Portage
Learning | 100% PASS
1. A probability is a numerical measure of likelihood that ranges from:
A) -1 to 1
B) 0 to 100
C) 0 to 1
D) 0 to ∞
Correct Answer: 0 to 1
Rationale: Probabilities are always between 0 and 1 inclusive. A probability of
0 indicates an impossible event, a probability of 1 indicates a certain event,
and values in between represent varying degrees of likelihood.
2. The set of all possible outcomes of a probability experiment is called the:
A) Event
B) Sample space
C) Population
D) Sample
Correct Answer: Sample space
Rationale: The sample space is the set of all possible outcomes of a
probability experiment. An event is a subset of the sample space. The
population and sample are statistical terms for groups of individuals.
3. The complement of an event A is:
A) The event that A occurs
,B) All outcomes in the sample space except A
C) The probability of A
D) The union of A with another event
Correct Answer: All outcomes in the sample space except A
Rationale: The complement of event A, denoted A^c, consists of all
outcomes in the sample space that are not in A. The complement rule states
P(A^c) = 1 - P(A).
4. The complement rule states that:
A) P(A) + P(B) = 1
B) P(A) = 1 - P(A^c)
C) P(A∩B) = 0
D) P(A∪B) = P(A) + P(B)
Correct Answer: P(A) = 1 - P(A^c)
Rationale: The complement rule states that the probability of an event is 1
minus the probability of its complement: P(A) = 1 - P(A^c). This is one of the
most fundamental probability rules.
5. If two events are mutually exclusive, then:
A) P(A∩B) = 1
B) P(A∩B) = P(A) × P(B)
C) P(A∩B) = 0
D) P(A∪B) = 0
, Correct Answer: P(A∩B) = 0
Rationale: Mutually exclusive events cannot occur at the same time, so their
intersection has probability 0. The addition rule for mutually exclusive events
simplifies to P(A∪B) = P(A) + P(B).
6. The addition rule for two events is:
A) P(A∪B) = P(A) + P(B)
B) P(A∪B) = P(A) + P(B) + P(A∩B)
C) P(A∪B) = P(A) + P(B) - P(A∩B)
D) P(A∪B) = P(A) × P(B)
Correct Answer: P(A∪B) = P(A) + P(B) - P(A∩B)
Rationale: The addition rule accounts for double-counting the intersection:
P(A∪B) = P(A) + P(B) - P(A∩B). When events are mutually exclusive, P(A∩B)
= 0, so the formula simplifies.
7. Suppose P(A) = 0.60, P(B) = 0.45, and P(A∪B) = 0.60. What is P(A∩B)?
A) 0.15
B) 0.45
C) 0.60
D) 1.05
Correct Answer: 0.45
Rationale: Using the addition rule: P(A∩B) = P(A) + P(B) - P(A∪B) = 0.60 +
0.45 - 0.60 = 0.45.
Learning | 100% PASS
1. A probability is a numerical measure of likelihood that ranges from:
A) -1 to 1
B) 0 to 100
C) 0 to 1
D) 0 to ∞
Correct Answer: 0 to 1
Rationale: Probabilities are always between 0 and 1 inclusive. A probability of
0 indicates an impossible event, a probability of 1 indicates a certain event,
and values in between represent varying degrees of likelihood.
2. The set of all possible outcomes of a probability experiment is called the:
A) Event
B) Sample space
C) Population
D) Sample
Correct Answer: Sample space
Rationale: The sample space is the set of all possible outcomes of a
probability experiment. An event is a subset of the sample space. The
population and sample are statistical terms for groups of individuals.
3. The complement of an event A is:
A) The event that A occurs
,B) All outcomes in the sample space except A
C) The probability of A
D) The union of A with another event
Correct Answer: All outcomes in the sample space except A
Rationale: The complement of event A, denoted A^c, consists of all
outcomes in the sample space that are not in A. The complement rule states
P(A^c) = 1 - P(A).
4. The complement rule states that:
A) P(A) + P(B) = 1
B) P(A) = 1 - P(A^c)
C) P(A∩B) = 0
D) P(A∪B) = P(A) + P(B)
Correct Answer: P(A) = 1 - P(A^c)
Rationale: The complement rule states that the probability of an event is 1
minus the probability of its complement: P(A) = 1 - P(A^c). This is one of the
most fundamental probability rules.
5. If two events are mutually exclusive, then:
A) P(A∩B) = 1
B) P(A∩B) = P(A) × P(B)
C) P(A∩B) = 0
D) P(A∪B) = 0
, Correct Answer: P(A∩B) = 0
Rationale: Mutually exclusive events cannot occur at the same time, so their
intersection has probability 0. The addition rule for mutually exclusive events
simplifies to P(A∪B) = P(A) + P(B).
6. The addition rule for two events is:
A) P(A∪B) = P(A) + P(B)
B) P(A∪B) = P(A) + P(B) + P(A∩B)
C) P(A∪B) = P(A) + P(B) - P(A∩B)
D) P(A∪B) = P(A) × P(B)
Correct Answer: P(A∪B) = P(A) + P(B) - P(A∩B)
Rationale: The addition rule accounts for double-counting the intersection:
P(A∪B) = P(A) + P(B) - P(A∩B). When events are mutually exclusive, P(A∩B)
= 0, so the formula simplifies.
7. Suppose P(A) = 0.60, P(B) = 0.45, and P(A∪B) = 0.60. What is P(A∩B)?
A) 0.15
B) 0.45
C) 0.60
D) 1.05
Correct Answer: 0.45
Rationale: Using the addition rule: P(A∩B) = P(A) + P(B) - P(A∪B) = 0.60 +
0.45 - 0.60 = 0.45.
