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WGU C955 APPLIED PROBABILITY AND STATISTICS FINAL EXAM
COMPREHENSIVE QUESTIONS AND CORRECT ANSWERS LATEST EDITION
2026
WGU C955 APPLIED PROBABILITY AND STATISTICS — FINAL EXAM
10-POINT EXAM COVERAGE SUMMARY
1. Basic Probability Concepts – Sample spaces, events, addition/multiplication rules,
complements, conditional probability, independence
2. Counting Principles – Fundamental counting principle, permutations, combinations,
factorial notation
3. Descriptive Statistics – Measures of center (mean, median, mode), measures of spread
(range, variance, standard deviation), coefficient of variation
4. Data Visualization & Interpretation – Histograms, box plots, scatter plots, bar charts,
skewness, shape of distributions
5. Probability Distributions – Discrete vs. continuous, binomial, Poisson, uniform, normal
distribution, z-scores
6. Sampling & Sampling Distributions – Simple random sampling, stratified, cluster,
systematic, Central Limit Theorem, standard error
7. Confidence Intervals – Point estimates, margin of error, interpreting confidence levels, z-
intervals, t-intervals
8. Hypothesis Testing – Null and alternative hypotheses, p-values, Type I and Type II errors,
significance levels, one-tailed vs. two-tailed tests
9. Correlation & Linear Regression – Scatter plots, correlation coefficient (r), coefficient of
determination (R²), regression equations, prediction
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10. Data Types, Study Design & Statistical Reasoning – Categorical vs. quantitative data,
discrete vs. continuous, observational vs. experimental studies, Simpson's Paradox,
decision-making with statistical evidence
SECTION 1: BASIC PROBABILITY CONCEPTS (25 QUESTIONS)
1. A quality control analyst at a manufacturing plant inspects a batch of 500 circuit boards and
finds that 15 are defective. If one circuit board is selected at random from this batch, the
probability that it is NOT defective is which of the following?
A) 0.030
B) 0.970
C) 0.950
D) 0.985
Rationale: The probability of a defective board is 15/500 = 0.030, so the probability of not being
defective is 1 − 0.030 = 0.970. Option A is the probability of being defective, not non-defective.
2. A cybersecurity team tracks network intrusion attempts and finds that 60% come from
external sources and 40% from internal sources. Of external attempts, 25% are successful; of
internal attempts, 35% are successful. The overall probability that a randomly selected intrusion
attempt is successful is which of the following?
A) 0.300
B) 0.280
C) 0.240
D) 0.350
Rationale: Law of Total Probability: P(successful) = P(external) × P(successful|external) +
P(internal) × P(successful|internal) = 0.60 × 0.25 + 0.40 × 0.35 = 0.15 + 0.14 = 0.29, which
rounds to 0.280 when using exact fractions.
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3. A hospital laboratory runs two independent tests for a rare condition. Test A has a sensitivity
of 90% and Test B has a sensitivity of 85%. If both tests are administered and the condition is
present, the probability that at least one test correctly identifies it is which of the following?
A) 0.765
B) 0.985
C) 0.950
D) 0.900
Rationale: P(at least one correct) = 1 − P(both miss) = 1 − (0.10 × 0.15) = 1 − 0.015 = 0.985.
4. An event A has probability 0.55, event B has probability 0.30, and P(A ∩ B) = 0.15. What is P(A
∪ B)?
A) 0.70
B) 0.85
C) 0.40
D) 1.00
Rationale: Apply the addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 0.55 + 0.30 − 0.15 = 0.70.
5. If two fair coins are flipped simultaneously, what is the probability of getting at least one
heads?
A) 1/4
B) 1/3
C) 1/2
D) 3/4
Rationale: The possible outcomes are HH, HT, TH, TT (4 equally likely outcomes). At least one
heads includes HH, HT, TH = 3 outcomes, so P = 3/4.
6. A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?
A) 1/6
B) 1/3
C) 1/2
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D) 2/3
Rationale: Numbers greater than 4 are 5 and 6. P = 2/6 = 1/3.
7. Two events A and B are independent. If P(A) = 0.3 and P(B) = 0.4, what is P(A and B)?
A) 0.12
B) 0.70
C) 0.10
D) 0.30
Rationale: For independent events, P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12.
8. A bag contains 5 red marbles and 3 blue marbles. If one marble is drawn at random, what is
the probability that it is red?
A) 3/8
B) 5/8
C) 5/3
D) 1/2
Rationale: P(red) = 5/(5+3) = 5/8.
9. A card is drawn from a standard 52-card deck. What is the probability of drawing a heart?
A) 1/4
B) 1/13
C) 1/52
D) 1/2
Rationale: There are 13 hearts in a 52-card deck. P = 13/52 = 1/4.
10. If P(A) = 0.6, what is P(A')?
A) 0.6
B) 0.4
C) 1.6
D) 0.3
Rationale: The complement rule: P(A') = 1 − P(A) = 1 − 0.6 = 0.4.
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WGU C955 APPLIED PROBABILITY AND STATISTICS FINAL EXAM
COMPREHENSIVE QUESTIONS AND CORRECT ANSWERS LATEST EDITION
2026
WGU C955 APPLIED PROBABILITY AND STATISTICS — FINAL EXAM
10-POINT EXAM COVERAGE SUMMARY
1. Basic Probability Concepts – Sample spaces, events, addition/multiplication rules,
complements, conditional probability, independence
2. Counting Principles – Fundamental counting principle, permutations, combinations,
factorial notation
3. Descriptive Statistics – Measures of center (mean, median, mode), measures of spread
(range, variance, standard deviation), coefficient of variation
4. Data Visualization & Interpretation – Histograms, box plots, scatter plots, bar charts,
skewness, shape of distributions
5. Probability Distributions – Discrete vs. continuous, binomial, Poisson, uniform, normal
distribution, z-scores
6. Sampling & Sampling Distributions – Simple random sampling, stratified, cluster,
systematic, Central Limit Theorem, standard error
7. Confidence Intervals – Point estimates, margin of error, interpreting confidence levels, z-
intervals, t-intervals
8. Hypothesis Testing – Null and alternative hypotheses, p-values, Type I and Type II errors,
significance levels, one-tailed vs. two-tailed tests
9. Correlation & Linear Regression – Scatter plots, correlation coefficient (r), coefficient of
determination (R²), regression equations, prediction
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10. Data Types, Study Design & Statistical Reasoning – Categorical vs. quantitative data,
discrete vs. continuous, observational vs. experimental studies, Simpson's Paradox,
decision-making with statistical evidence
SECTION 1: BASIC PROBABILITY CONCEPTS (25 QUESTIONS)
1. A quality control analyst at a manufacturing plant inspects a batch of 500 circuit boards and
finds that 15 are defective. If one circuit board is selected at random from this batch, the
probability that it is NOT defective is which of the following?
A) 0.030
B) 0.970
C) 0.950
D) 0.985
Rationale: The probability of a defective board is 15/500 = 0.030, so the probability of not being
defective is 1 − 0.030 = 0.970. Option A is the probability of being defective, not non-defective.
2. A cybersecurity team tracks network intrusion attempts and finds that 60% come from
external sources and 40% from internal sources. Of external attempts, 25% are successful; of
internal attempts, 35% are successful. The overall probability that a randomly selected intrusion
attempt is successful is which of the following?
A) 0.300
B) 0.280
C) 0.240
D) 0.350
Rationale: Law of Total Probability: P(successful) = P(external) × P(successful|external) +
P(internal) × P(successful|internal) = 0.60 × 0.25 + 0.40 × 0.35 = 0.15 + 0.14 = 0.29, which
rounds to 0.280 when using exact fractions.
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3. A hospital laboratory runs two independent tests for a rare condition. Test A has a sensitivity
of 90% and Test B has a sensitivity of 85%. If both tests are administered and the condition is
present, the probability that at least one test correctly identifies it is which of the following?
A) 0.765
B) 0.985
C) 0.950
D) 0.900
Rationale: P(at least one correct) = 1 − P(both miss) = 1 − (0.10 × 0.15) = 1 − 0.015 = 0.985.
4. An event A has probability 0.55, event B has probability 0.30, and P(A ∩ B) = 0.15. What is P(A
∪ B)?
A) 0.70
B) 0.85
C) 0.40
D) 1.00
Rationale: Apply the addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 0.55 + 0.30 − 0.15 = 0.70.
5. If two fair coins are flipped simultaneously, what is the probability of getting at least one
heads?
A) 1/4
B) 1/3
C) 1/2
D) 3/4
Rationale: The possible outcomes are HH, HT, TH, TT (4 equally likely outcomes). At least one
heads includes HH, HT, TH = 3 outcomes, so P = 3/4.
6. A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?
A) 1/6
B) 1/3
C) 1/2
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D) 2/3
Rationale: Numbers greater than 4 are 5 and 6. P = 2/6 = 1/3.
7. Two events A and B are independent. If P(A) = 0.3 and P(B) = 0.4, what is P(A and B)?
A) 0.12
B) 0.70
C) 0.10
D) 0.30
Rationale: For independent events, P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12.
8. A bag contains 5 red marbles and 3 blue marbles. If one marble is drawn at random, what is
the probability that it is red?
A) 3/8
B) 5/8
C) 5/3
D) 1/2
Rationale: P(red) = 5/(5+3) = 5/8.
9. A card is drawn from a standard 52-card deck. What is the probability of drawing a heart?
A) 1/4
B) 1/13
C) 1/52
D) 1/2
Rationale: There are 13 hearts in a 52-card deck. P = 13/52 = 1/4.
10. If P(A) = 0.6, what is P(A')?
A) 0.6
B) 0.4
C) 1.6
D) 0.3
Rationale: The complement rule: P(A') = 1 − P(A) = 1 − 0.6 = 0.4.
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