Sophia Statistics – Unit 3 Mastery Assessment
Complete Milestone Exam Actual Exam – Complete
Questions and Answers with Detailed Rationales –
Pass Guaranteed – A+ Graded
Section 1: Basic Probability & The Addition Rule
Q1: A quality control inspector at a manufacturing plant randomly selects one item from
a batch of 200. She knows that 15 items are defective and the rest are good. If she
picks one item at random, what is the probability that it is not defective?
A. 15/200
B. 1 – 15/185
C. 185/200 [CORRECT]
D. 15/185
Correct Answer: C
Rationale: The best answer is 185/200. Since 15 out of 200 are defective, that leaves
185 good items. You could also get here using the complement rule: P(not defective) =
1 – P(defective) = 1 – 15/200 = 185/200. Either way, you're looking at the proportion of
non-defective items in the whole batch.
,Q2: Which of the following statements about probability is always true?
A. The probability of an event and the probability of its complement add up to 100.
B. If two events are mutually exclusive, they must also be independent.
C. The probability of any event must be between 0 and 1, inclusive. [CORRECT]
D. Empirical probability is calculated by dividing the number of possible outcomes by
the number of favorable outcomes.
Correct Answer: C
Rationale: This choice is correct because probability values are always bounded
between 0 (impossible) and 1 (certain), inclusive. That's a fundamental rule of
probability theory. The complement rule adds to 1, not 100; mutually exclusive events
with positive probability cannot be independent; and empirical probability uses relative
frequency (favorable over total), not the reverse.
Q3: At a community college, 120 students are enrolled in statistics, 80 are enrolled in
psychology, and 30 are enrolled in both. If a student is selected at random, what is the
probability they are in statistics or psychology?
A. 200/200 = 1
B. (120 + 80) / 200
C. (120 + 80 – 30) / 170
D. (120 + 80 – 30) / 200 [CORRECT]
Correct Answer: D
, Rationale: The best answer is (120 + 80 – 30) / 200. You need the addition rule here: P(S
or P) = P(S) + P(P) – P(S and P). The 30 students taking both got counted twice, so
subtract them once. The total number of students is 120 + 80 – 30 = 170, but the
probability is 170 out of the total 200 students, giving 170/200 or 0.85.
Q4: A card is drawn from a standard 52-card deck. Let Event A be "drawing a heart" and
Event B be "drawing a red card." Which statement is correct?
A. A and B are mutually exclusive because hearts and red cards are different categories.
B. A and B are not mutually exclusive because every heart is also a red card. [CORRECT]
C. A and B are independent because knowing the card is red doesn't change the
probability it's a heart.
D. A and B are complementary because a card is either a heart or a red card.
Correct Answer: B
Rationale: This choice is correct because all hearts are red cards, so if you draw a heart,
you have automatically drawn a red card too. The events can definitely occur
together—in fact, one is contained within the other. They're not mutually exclusive, and
they're not independent either because P(heart | red) = 1/2, which is different from
P(heart) = 1/4.
Q5: In a survey of 500 adults, 320 said they prefer online shopping, 150 said they prefer
in-store shopping, and 30 said they have no preference. If one person is selected at
random, what is the empirical probability that they prefer in-store shopping?
A. 150/500 [CORRECT]
Complete Milestone Exam Actual Exam – Complete
Questions and Answers with Detailed Rationales –
Pass Guaranteed – A+ Graded
Section 1: Basic Probability & The Addition Rule
Q1: A quality control inspector at a manufacturing plant randomly selects one item from
a batch of 200. She knows that 15 items are defective and the rest are good. If she
picks one item at random, what is the probability that it is not defective?
A. 15/200
B. 1 – 15/185
C. 185/200 [CORRECT]
D. 15/185
Correct Answer: C
Rationale: The best answer is 185/200. Since 15 out of 200 are defective, that leaves
185 good items. You could also get here using the complement rule: P(not defective) =
1 – P(defective) = 1 – 15/200 = 185/200. Either way, you're looking at the proportion of
non-defective items in the whole batch.
,Q2: Which of the following statements about probability is always true?
A. The probability of an event and the probability of its complement add up to 100.
B. If two events are mutually exclusive, they must also be independent.
C. The probability of any event must be between 0 and 1, inclusive. [CORRECT]
D. Empirical probability is calculated by dividing the number of possible outcomes by
the number of favorable outcomes.
Correct Answer: C
Rationale: This choice is correct because probability values are always bounded
between 0 (impossible) and 1 (certain), inclusive. That's a fundamental rule of
probability theory. The complement rule adds to 1, not 100; mutually exclusive events
with positive probability cannot be independent; and empirical probability uses relative
frequency (favorable over total), not the reverse.
Q3: At a community college, 120 students are enrolled in statistics, 80 are enrolled in
psychology, and 30 are enrolled in both. If a student is selected at random, what is the
probability they are in statistics or psychology?
A. 200/200 = 1
B. (120 + 80) / 200
C. (120 + 80 – 30) / 170
D. (120 + 80 – 30) / 200 [CORRECT]
Correct Answer: D
, Rationale: The best answer is (120 + 80 – 30) / 200. You need the addition rule here: P(S
or P) = P(S) + P(P) – P(S and P). The 30 students taking both got counted twice, so
subtract them once. The total number of students is 120 + 80 – 30 = 170, but the
probability is 170 out of the total 200 students, giving 170/200 or 0.85.
Q4: A card is drawn from a standard 52-card deck. Let Event A be "drawing a heart" and
Event B be "drawing a red card." Which statement is correct?
A. A and B are mutually exclusive because hearts and red cards are different categories.
B. A and B are not mutually exclusive because every heart is also a red card. [CORRECT]
C. A and B are independent because knowing the card is red doesn't change the
probability it's a heart.
D. A and B are complementary because a card is either a heart or a red card.
Correct Answer: B
Rationale: This choice is correct because all hearts are red cards, so if you draw a heart,
you have automatically drawn a red card too. The events can definitely occur
together—in fact, one is contained within the other. They're not mutually exclusive, and
they're not independent either because P(heart | red) = 1/2, which is different from
P(heart) = 1/4.
Q5: In a survey of 500 adults, 320 said they prefer online shopping, 150 said they prefer
in-store shopping, and 30 said they have no preference. If one person is selected at
random, what is the empirical probability that they prefer in-store shopping?
A. 150/500 [CORRECT]
