WGU C207 DATA-DRIVEN DECISION MAKING OA
PRACTICE QUESTIONS, VERIFIED ANSWERS &
RATIONALES 100% CORRECT! (Probability Concepts)
Question 1 (Multiple Choice)
A quality control inspector finds that the probability of a circuit board failing inspection is
0.08. What is the probability that a randomly selected circuit board passes inspection
(the complement event)?
● A. 0.08
● B. 0.92
● C. 1.08
● D. 0.00
Correct Answer: B. 0.92
Rationale: The sum of the probabilities of all possible mutually exclusive outcomes
must equal 1.0. The complement of an event failing is the event succeeding. Therefore,
P(Pass)=1−P(Fail)=1−0.08=0.92.
Question 2 (Multiple Choice)
A retail store manager tracks customer purchases and notes that 40% of customers buy
coffee (C) and 25% buy a pastry (P). Furthermore, 10% of customers buy both coffee
and a pastry (C and P). What is the probability that a randomly chosen customer buys
either coffee or a pastry (C or P)?
● A. 0.65
● B. 0.55
● C. 0.10
● D. 0.75
Correct Answer: B. 0.55
Rationale: Using the general addition rule: P(C or P)=P(C)+P(P)−P(C and
P)=0.40+0.25−0.10=0.55.
Question 3 (Multiple Choice)
, An online retailer determines that the probability of a visitor making a purchase on their
website is 0.03. If two independent visitors arrive on the site, what is the probability that
both visitors make a purchase?
● A. 0.06
● B. 0.0009
● C. 0.9700
● D. 0.0300
Correct Answer: B. 0.0009
Rationale: For independent events, the multiplication rule states that the probability of
both events occurring is the product of their individual probabilities: P(A and
B)=P(A)×P(B)=0.03×0.03=0.0009.
Question 4 (Multiple Choice)
A manufacturing plant has two assembly lines producing widgets. Line A produces 60%
of the total widgets, and Line B produces 40%. The probability that a widget from Line A
is defective is 0.02, and for Line B it is 0.05. If a randomly selected widget is found to be
defective, what concept is used to calculate the exact probability that it came from Line
B?
● A. The Central Limit Theorem
● B. Bayes' Theorem (Conditional Probability)
● C. The Chi-Square test of independence
● D. Simple linear regression slope estimation
Correct Answer: B. Bayes' Theorem (Conditional Probability)
Rationale: Bayes' Theorem is used to calculate conditional probability—specifically,
finding the probability of a prior cause (coming from Line B) given an observed outcome
(the widget is defective).
Question 5 (Multiple Choice)
A human resources department reviews applicant data and finds that 70% of applicants
have a college degree (D) and 40% have management experience (M). If having a
degree and having management experience are independent events, what is the
probability that an applicant has both a college degree and management experience?
● A. 1.10
● B. 0.28
PRACTICE QUESTIONS, VERIFIED ANSWERS &
RATIONALES 100% CORRECT! (Probability Concepts)
Question 1 (Multiple Choice)
A quality control inspector finds that the probability of a circuit board failing inspection is
0.08. What is the probability that a randomly selected circuit board passes inspection
(the complement event)?
● A. 0.08
● B. 0.92
● C. 1.08
● D. 0.00
Correct Answer: B. 0.92
Rationale: The sum of the probabilities of all possible mutually exclusive outcomes
must equal 1.0. The complement of an event failing is the event succeeding. Therefore,
P(Pass)=1−P(Fail)=1−0.08=0.92.
Question 2 (Multiple Choice)
A retail store manager tracks customer purchases and notes that 40% of customers buy
coffee (C) and 25% buy a pastry (P). Furthermore, 10% of customers buy both coffee
and a pastry (C and P). What is the probability that a randomly chosen customer buys
either coffee or a pastry (C or P)?
● A. 0.65
● B. 0.55
● C. 0.10
● D. 0.75
Correct Answer: B. 0.55
Rationale: Using the general addition rule: P(C or P)=P(C)+P(P)−P(C and
P)=0.40+0.25−0.10=0.55.
Question 3 (Multiple Choice)
, An online retailer determines that the probability of a visitor making a purchase on their
website is 0.03. If two independent visitors arrive on the site, what is the probability that
both visitors make a purchase?
● A. 0.06
● B. 0.0009
● C. 0.9700
● D. 0.0300
Correct Answer: B. 0.0009
Rationale: For independent events, the multiplication rule states that the probability of
both events occurring is the product of their individual probabilities: P(A and
B)=P(A)×P(B)=0.03×0.03=0.0009.
Question 4 (Multiple Choice)
A manufacturing plant has two assembly lines producing widgets. Line A produces 60%
of the total widgets, and Line B produces 40%. The probability that a widget from Line A
is defective is 0.02, and for Line B it is 0.05. If a randomly selected widget is found to be
defective, what concept is used to calculate the exact probability that it came from Line
B?
● A. The Central Limit Theorem
● B. Bayes' Theorem (Conditional Probability)
● C. The Chi-Square test of independence
● D. Simple linear regression slope estimation
Correct Answer: B. Bayes' Theorem (Conditional Probability)
Rationale: Bayes' Theorem is used to calculate conditional probability—specifically,
finding the probability of a prior cause (coming from Line B) given an observed outcome
(the widget is defective).
Question 5 (Multiple Choice)
A human resources department reviews applicant data and finds that 70% of applicants
have a college degree (D) and 40% have management experience (M). If having a
degree and having management experience are independent events, what is the
probability that an applicant has both a college degree and management experience?
● A. 1.10
● B. 0.28
