WGU C955 Applied Probability and Statistics Final Exam 2026/2027 | 100 Questions & Answers with Explanations

WGU C955 Applied Probability and Statistics Final Exam (Latest
2026/2027 Update)
100 Questions & Answers with Concise Rationales


1. A box contains 8 red marbles and 12 blue marbles. What is the probability of
randomly selecting a red marble?
A. 0.20
B. 0.40
C. 0.60
D. 0.80
Correct Answer: B. 0.40
Explanation: There are 20 total marbles, 8 of which are red. P(red) = 8/20 = 0.40.


2. A fair six-sided die is rolled once. What is the probability of rolling a number greater
than 4?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Correct Answer: B. 1/3
Explanation: The outcomes greater than 4 are 5 and 6, giving 2 favorable outcomes out of 6.
P = 2/6 = 1/3.


3. A survey of 400 employees found that 280 prefer remote work. What is the empirical
probability that a randomly selected employee does NOT prefer remote work?
A. 0.30
B. 0.40
C. 0.70
D. 0.80
Correct Answer: A. 0.30
Explanation: P(prefers remote) = 280/400 = 0.70. By the complement rule, P(does not prefer)
= 1 - 0.70 = 0.30.


4. Events A and B are independent, with P(A) = 0.4 and P(B) = 0.5. Find P(A and B).
A. 0.10
B. 0.20
C. 0.45
D. 0.90
Correct Answer: B. 0.20

,Explanation: For independent events, P(A and B) = P(A) x P(B) = 0.4 x 0.5 = 0.20.


5. Two cards are drawn without replacement from a standard 52-card deck. What is the
probability that both cards are aces?
A. 1/13
B. 1/221
C. 1/26
D. 4/51
Correct Answer: B. 1/221
Explanation: P(first ace) = 4/52. P(second ace | first ace) = 3/51. Multiplying gives (4/52)(3/51)
= 12/2652 = 1/221.


6. What is the complement of an event with probability 0.35?
A. 0.35
B. 0.65
C. 1.35
D. 0
Correct Answer: B. 0.65
Explanation: The complement rule states P(not A) = 1 - P(A). So 1 - 0.35 = 0.65.


7. A bag contains 5 green and 7 yellow balls. Two balls are drawn without replacement.
What is the probability that the first ball is green and the second is yellow?
A. 0.265
B. 0.417
C. 0.583
D. 0.300
Correct Answer: A. 0.265
Explanation: P(green first) = 5/12. P(yellow second | green first) = 7/11. Multiplying:
(5/12)(7/11) = 35/132 ≈ 0.265.


8. Two dependent events A and B have P(A) = 0.6 and P(B|A) = 0.3. Find P(A and B).
A. 0.18
B. 0.30
C. 0.50
D. 0.90
Correct Answer: A. 0.18
Explanation: For dependent events, P(A and B) = P(A) x P(B|A) = 0.6 x 0.3 = 0.18.

, 9. In a class of 30 students, 18 take Math, 12 take Science, and 6 take both subjects.
What is the probability that a randomly selected student takes Math or Science?
A. 0.60
B. 0.70
C. 0.80
D. 1.00
Correct Answer: C. 0.80
Explanation: Using the addition rule: P(M or S) = P(M) + P(S) - P(M and S) = 18/30 + 12/30 -
6/30 = 24/30 = 0.80.


10. A production line has a 5% defect rate. If two items are selected independently, what
is the probability that both are defective?
A. 0.0025
B. 0.0500
C. 0.1000
D. 0.2500
Correct Answer: A. 0.0025
Explanation: For independent events, multiply the probabilities: 0.05 x 0.05 = 0.0025.


11. If P(A) = 0.3, what is P(not A)?
A. 0.30
B. 0.70
C. 0.03
D. 1.30
Correct Answer: B. 0.70
Explanation: By the complement rule, P(not A) = 1 - P(A) = 1 - 0.30 = 0.70.


12. A diagnostic test correctly detects a disease in 90% of patients who have it, and the
disease occurs in 2% of the population. If a patient tests positive, which concept is
needed to determine the actual probability that the patient has the disease?
A. Law of large numbers
B. Bayes' theorem
C. Central limit theorem
D. Empirical rule
Correct Answer: B. Bayes' theorem
Explanation: Bayes' theorem is used to update the probability of an event (having the
disease) given new evidence (a positive test result), incorporating both test accuracy and the
base rate of the disease.