Statistics Module 2 Exam Actual Exam 2026/2027
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Section 1: Probability Concepts (Questions 1–10)
Q1: In a standard deck of 52 playing cards, what is the probability of drawing a face card (jack, queen, or
king)?
A. 3/52
B. 1/13
C. 3/13 [CORRECT]
D. 1/4
Correct Answer: C
Rationale: There are 12 face cards in a deck (3 per suit × 4 suits), so the probability is 12/52, which
reduces to 3/13.
Q2: If two events A and B are mutually exclusive, which of the following must be true?
A. P(A ∩ B) = P(A) × P(B)
B. P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
C. P(A ∩ B) = 0 *CORRECT+
D. P(A) = P(B)
Correct Answer: C
Rationale: Mutually exclusive events cannot occur at the same time, so their intersection has probability
zero, which is the defining property that separates them from independent events.
Q3: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at
random, what is the probability that it is either red or blue?
A. 5/10
B. 8/10 [CORRECT]
C. 15/10
,D. 3/10
Correct Answer: B
Rationale: There are 8 favorable outcomes (5 red + 3 blue) out of 10 total marbles, giving a probability
of 8/10 or 4/5.
Q4: The probability that a patient has diabetes is 0.15, and the probability that a patient has
hypertension is 0.30. If these conditions are independent, what is the probability that a randomly
selected patient has both diabetes and hypertension?
A. 0.45
B. 0.15
C. 0.045 [CORRECT]
D. 0.015
Correct Answer: C
Rationale: For independent events, you multiply their probabilities: 0.15 × 0.30 = 0.045.
Q5: In a clinical trial, the probability that a new drug is effective is 0.70. Given that the drug is effective,
the probability that a patient shows significant improvement is 0.85. What is the probability that the
drug is effective AND the patient shows significant improvement?
A. 0.70
B. 0.85
C. 0.595 [CORRECT]
D. 0.155
Correct Answer: C
Rationale: Using the multiplication rule for conditional probability, P(effective ∩ improvement) =
P(effective) × P(improvement | effective) = 0.70 × 0.85 = 0.595.
Q6: A diagnostic test for a disease has a sensitivity of 95% and a specificity of 90%. If the prevalence of
the disease in the population is 5%, what is the positive predictive value (PPV) of the test? (Use Bayes'
theorem.)
A. 95%
B. 33.3% [CORRECT]
C. 90%
D. 5%
Correct Answer: B
Rationale: Using Bayes' theorem with a 5% prevalence, the PPV works out to roughly 33% because even
with good specificity, the low prevalence means most positive results are false positives.
, Q7: If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2, what is P(A | B)?
A. 0.4
B. 0.5
C. 0.4
D. 0.4 [CORRECT]
Correct Answer: D
Rationale: The conditional probability P(A | B) equals P(A ∩ B) divided by P(B), so 0..5 = 0.4.
Q8: A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?
A. 1/6 [CORRECT]
B. 1/12
C. 1/36
D. 7/36
Correct Answer: A
Rationale: There are 6 ways to roll a sum of 7 out of 36 possible outcomes when rolling two dice, giving
a probability of 6/36 = 1/6.
Q9: The complement rule states that for any event A, P(A') = 1 − P(A). If the probability of rain tomorrow
is 0.35, what is the probability that it does NOT rain?
A. 0.35
B. 0.65 [CORRECT]
C. 1.35
D. 0.50
Correct Answer: B
Rationale: Using the complement rule, the probability of no rain is simply 1 − 0.35 = 0.65.
Q10: In a hospital, 60% of patients are male and 40% are female. Among male patients, 30% have
hypertension; among female patients, 25% have hypertension. What is the overall probability that a
randomly selected patient has hypertension?
A. 0.55
B. 0.28 [CORRECT]
C. 0.30
D. 0.15
100% Verified | Detailed Rationales – Pass
Guaranteed – A+ Graded
Section 1: Probability Concepts (Questions 1–10)
Q1: In a standard deck of 52 playing cards, what is the probability of drawing a face card (jack, queen, or
king)?
A. 3/52
B. 1/13
C. 3/13 [CORRECT]
D. 1/4
Correct Answer: C
Rationale: There are 12 face cards in a deck (3 per suit × 4 suits), so the probability is 12/52, which
reduces to 3/13.
Q2: If two events A and B are mutually exclusive, which of the following must be true?
A. P(A ∩ B) = P(A) × P(B)
B. P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
C. P(A ∩ B) = 0 *CORRECT+
D. P(A) = P(B)
Correct Answer: C
Rationale: Mutually exclusive events cannot occur at the same time, so their intersection has probability
zero, which is the defining property that separates them from independent events.
Q3: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at
random, what is the probability that it is either red or blue?
A. 5/10
B. 8/10 [CORRECT]
C. 15/10
,D. 3/10
Correct Answer: B
Rationale: There are 8 favorable outcomes (5 red + 3 blue) out of 10 total marbles, giving a probability
of 8/10 or 4/5.
Q4: The probability that a patient has diabetes is 0.15, and the probability that a patient has
hypertension is 0.30. If these conditions are independent, what is the probability that a randomly
selected patient has both diabetes and hypertension?
A. 0.45
B. 0.15
C. 0.045 [CORRECT]
D. 0.015
Correct Answer: C
Rationale: For independent events, you multiply their probabilities: 0.15 × 0.30 = 0.045.
Q5: In a clinical trial, the probability that a new drug is effective is 0.70. Given that the drug is effective,
the probability that a patient shows significant improvement is 0.85. What is the probability that the
drug is effective AND the patient shows significant improvement?
A. 0.70
B. 0.85
C. 0.595 [CORRECT]
D. 0.155
Correct Answer: C
Rationale: Using the multiplication rule for conditional probability, P(effective ∩ improvement) =
P(effective) × P(improvement | effective) = 0.70 × 0.85 = 0.595.
Q6: A diagnostic test for a disease has a sensitivity of 95% and a specificity of 90%. If the prevalence of
the disease in the population is 5%, what is the positive predictive value (PPV) of the test? (Use Bayes'
theorem.)
A. 95%
B. 33.3% [CORRECT]
C. 90%
D. 5%
Correct Answer: B
Rationale: Using Bayes' theorem with a 5% prevalence, the PPV works out to roughly 33% because even
with good specificity, the low prevalence means most positive results are false positives.
, Q7: If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2, what is P(A | B)?
A. 0.4
B. 0.5
C. 0.4
D. 0.4 [CORRECT]
Correct Answer: D
Rationale: The conditional probability P(A | B) equals P(A ∩ B) divided by P(B), so 0..5 = 0.4.
Q8: A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?
A. 1/6 [CORRECT]
B. 1/12
C. 1/36
D. 7/36
Correct Answer: A
Rationale: There are 6 ways to roll a sum of 7 out of 36 possible outcomes when rolling two dice, giving
a probability of 6/36 = 1/6.
Q9: The complement rule states that for any event A, P(A') = 1 − P(A). If the probability of rain tomorrow
is 0.35, what is the probability that it does NOT rain?
A. 0.35
B. 0.65 [CORRECT]
C. 1.35
D. 0.50
Correct Answer: B
Rationale: Using the complement rule, the probability of no rain is simply 1 − 0.35 = 0.65.
Q10: In a hospital, 60% of patients are male and 40% are female. Among male patients, 30% have
hypertension; among female patients, 25% have hypertension. What is the overall probability that a
randomly selected patient has hypertension?
A. 0.55
B. 0.28 [CORRECT]
C. 0.30
D. 0.15
