MATH 225N Week 4 Statistics Quiz Solutions
Actual Exam 2026/2027 – Attempt Score A+
with Detailed Rationales – Pass Guaranteed –
A+ Graded
Probability Fundamentals & Rules
Q1: Which of the following statements best describes the difference between classical
and empirical probability?
A. Classical probability is based on observed data, while empirical probability is based
on theoretical reasoning
B. Empirical probability can only be used for mutually exclusive events, while classical
probability applies to all events
C. Classical probability requires a large sample size, whereas empirical probability
works well with small samples
D. Classical probability relies on equally likely outcomes in a sample space, while
empirical probability relies on the actual frequency of events from observed data
[CORRECT]
Correct Answer: D
Rationale: The best answer is D because classical probability assumes you know the
theoretical likelihood of every outcome ahead of time (like flipping a fair coin), whereas
empirical probability is calculated by actually running an experiment or observing
real-world data to see how often something happens.
Q2: A clinic finds that 15% of its patients are late for their appointments. What is the
probability that a randomly selected patient will arrive on time?
A. 0.15
B. 0.85 [CORRECT]
C. 0.50
D. 1.15
Correct Answer: B
Rationale: This choice is correct because the complement rule states that the probability
of an event not happening is simply 1 minus the probability that it does happen, so 1 -
0.15 gives us 0.85.
, Q3: A hospital ward has 30 nurses. 15 are BSN-prepared, 10 are ADN-prepared, and 5
have a diploma. If a nurse is selected at random to lead a committee, what is the
probability they are either BSN or ADN-prepared, assuming these categories are
mutually exclusive?
A. 5/6 [CORRECT]
B. 25/30
C. 1/3
D. 15/30
Correct Answer: A
Rationale: The best answer is A because since a nurse cannot hold two different
entry-level degrees at once, these are mutually exclusive events, meaning you just add
their individual probabilities together (15/30 + 10/30 = 25/30, which simplifies to 5/6)
without worrying about an overlap.
Q4: In a sample of 500 adults, 220 have high cholesterol and 160 have high blood
pressure. 80 have both conditions. What is the probability that a randomly selected
adult has either high cholesterol or high blood pressure?
A. 0.60 [CORRECT]
B. 0.76
C. 0.44
D. 0.16
Correct Answer: A
Rationale: This aligns with the general addition rule, which requires subtracting the
overlap so you don't count the 80 people with both conditions twice, giving us (220 +
160 - 80) / 500 = = 0.60.
Q5: Two separate IV pumps are used to deliver medications to a patient. Pump A has a
5% chance of alarming in a shift, and Pump B has a 10% chance. Assuming the pumps
operate independently, what is the probability that both pumps will alarm during the
shift?
A. 0.15
B. 0.005 [CORRECT]
C. 0.50
D. 0.075
Correct Answer: B
Rationale: This choice is correct because for independent events, the multiplication rule
says you multiply the individual probabilities to find the probability of both occurring, so
0.05 multiplied by 0.10 equals 0.005.
Q6: What is the correct formula for calculating conditional probability, P(A|B)?
A. P(A) × P(B)
Actual Exam 2026/2027 – Attempt Score A+
with Detailed Rationales – Pass Guaranteed –
A+ Graded
Probability Fundamentals & Rules
Q1: Which of the following statements best describes the difference between classical
and empirical probability?
A. Classical probability is based on observed data, while empirical probability is based
on theoretical reasoning
B. Empirical probability can only be used for mutually exclusive events, while classical
probability applies to all events
C. Classical probability requires a large sample size, whereas empirical probability
works well with small samples
D. Classical probability relies on equally likely outcomes in a sample space, while
empirical probability relies on the actual frequency of events from observed data
[CORRECT]
Correct Answer: D
Rationale: The best answer is D because classical probability assumes you know the
theoretical likelihood of every outcome ahead of time (like flipping a fair coin), whereas
empirical probability is calculated by actually running an experiment or observing
real-world data to see how often something happens.
Q2: A clinic finds that 15% of its patients are late for their appointments. What is the
probability that a randomly selected patient will arrive on time?
A. 0.15
B. 0.85 [CORRECT]
C. 0.50
D. 1.15
Correct Answer: B
Rationale: This choice is correct because the complement rule states that the probability
of an event not happening is simply 1 minus the probability that it does happen, so 1 -
0.15 gives us 0.85.
, Q3: A hospital ward has 30 nurses. 15 are BSN-prepared, 10 are ADN-prepared, and 5
have a diploma. If a nurse is selected at random to lead a committee, what is the
probability they are either BSN or ADN-prepared, assuming these categories are
mutually exclusive?
A. 5/6 [CORRECT]
B. 25/30
C. 1/3
D. 15/30
Correct Answer: A
Rationale: The best answer is A because since a nurse cannot hold two different
entry-level degrees at once, these are mutually exclusive events, meaning you just add
their individual probabilities together (15/30 + 10/30 = 25/30, which simplifies to 5/6)
without worrying about an overlap.
Q4: In a sample of 500 adults, 220 have high cholesterol and 160 have high blood
pressure. 80 have both conditions. What is the probability that a randomly selected
adult has either high cholesterol or high blood pressure?
A. 0.60 [CORRECT]
B. 0.76
C. 0.44
D. 0.16
Correct Answer: A
Rationale: This aligns with the general addition rule, which requires subtracting the
overlap so you don't count the 80 people with both conditions twice, giving us (220 +
160 - 80) / 500 = = 0.60.
Q5: Two separate IV pumps are used to deliver medications to a patient. Pump A has a
5% chance of alarming in a shift, and Pump B has a 10% chance. Assuming the pumps
operate independently, what is the probability that both pumps will alarm during the
shift?
A. 0.15
B. 0.005 [CORRECT]
C. 0.50
D. 0.075
Correct Answer: B
Rationale: This choice is correct because for independent events, the multiplication rule
says you multiply the individual probabilities to find the probability of both occurring, so
0.05 multiplied by 0.10 equals 0.005.
Q6: What is the correct formula for calculating conditional probability, P(A|B)?
A. P(A) × P(B)
