AP Statistics Practice Quiz: Independent Events and Unions of Events
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 11 questions to check your progress.
Question 1 of 11
All Questions (11)
A) 0.15
B) 0.80
C) 0.65
D) 0.20
Correct Answer: A
According to the provided content, if events A and B are independent, then P(A and B) = P(A) * P(B). Therefore, P(A and B) = 0.3 * 0.5 = 0.15.
A) 1.0
B) 0.24
C) 0.8
D) 1.2
Correct Answer: C
The addition rule states that P(A or B) = P(A) + P(B) - P(A and B). Plugging in the given values: P(A or B) = 0.6 + 0.4 - 0.2 = 0.8.
A) 0.90
B) 0.14
C) 0.76
D) 0.50
Correct Answer: C
The probability that at least one event occurs is P(A or B). First, since the events are independent, we find P(A and B) = P(A) * P(B) = 0.7 * 0.2 = 0.14. Then, using the addition rule, P(A or B) = P(A) + P(B) - P(A and B) = 0.7 + 0.2 - 0.14 = 0.76.
A) P(A and B) = P(A) + P(B)
B) P(A|B) = P(B)
C) P(A or B) = P(A) + P(B)
D) P(B|A) = P(B)
Correct Answer: D
The provided content states that events A and B are independent if knowing A occurs does not change the probability of B. This is mathematically expressed as P(B|A) = P(B). The other options are incorrect formulas for independence or union.
A) Only event A occurs.
B) Both events A and B occur simultaneously.
C) Neither event A nor event B occurs.
D) Event A occurs, event B occurs, or both occur.
Correct Answer: D
As stated in the provided content, 'The probability of the union of A and B, P(A or B), is the probability that A, B, or both occur.'
A) Events A and B are independent because P(A) + P(B) > P(A or B).
B) Events A and B are not independent because P(A) * P(B) is not equal to P(A and B).
C) Events A and B are independent because P(A) * P(B) = 0.2.
D) Events A and B are not independent because P(A) + P(B) is not equal to 1.
Correct Answer: B
First, use the addition rule to find the actual P(A and B): P(A and B) = P(A) + P(B) - P(A or B) = 0.5 + 0.4 - 0.7 = 0.2. For the events to be independent, P(A and B) must equal P(A) * P(B). Here, P(A) * P(B) = 0.5 * 0.4 = 0.2. Since P(A and B) is equal to P(A) * P(B), the events are actually independent. Let me re-evaluate the question and options. Ah, the explanation logic must be precise. Let's re-calculate: P(A and B) = 0.5 + 0.4 - 0.7 = 0.2. The test for independence is P(A) * P(B) = 0.5 * 0.4 = 0.2. Since 0.2 = 0.2, the events ARE independent. My options are flawed. Let me fix the question's numbers. Let P(A or B) = 0.8. Then P(A and B) = 0.5 + 0.4 - 0.8 = 0.1. P(A) * P(B) = 0.5 * 0.4 = 0.2. Since 0.1 is not equal to 0.2, the events are not independent. Let's rewrite the question with P(A or B) = 0.8.
A) Events A and B are independent because P(A) + P(B) > P(A or B).
B) Events A and B are not independent because P(A) * P(B) is not equal to P(A and B).
C) Events A and B are independent because P(A and B) = 0.1.
D) Events A and B are not independent because P(A) + P(B) is not equal to 1.
Correct Answer: B
First, use the addition rule to find the actual P(A and B): P(A and B) = P(A) + P(B) - P(A or B) = 0.5 + 0.4 - 0.8 = 0.1. For the events to be independent, P(A and B) must equal P(A) * P(B). Here, P(A) * P(B) = 0.5 * 0.4 = 0.2. Since 0.1 is not equal to 0.2, the events are not independent.
A) To ensure the final probability is less than 1.
B) Because P(A and B) is always a negative value.
C) To correct for the outcomes in the intersection of A and B being counted twice when P(A) and P(B) are added.
D) Because this term only applies to independent events.
Correct Answer: C
The term P(A and B) represents the probability of the intersection of A and B (both occurring). When P(A) and P(B) are added, the probabilities of the outcomes in this intersection are included in both terms. Therefore, P(A and B) must be subtracted to avoid double-counting.
A) 1.70
B) 0.98
C) 0.72
D) 0.85
Correct Answer: C
Let A be the event of passing the Math test and B be the event of passing the Science test. The problem states the events are independent. The probability of passing both is P(A and B). For independent events, P(A and B) = P(A) * P(B). Therefore, the probability is 0.8 * 0.9 = 0.72.
A) The events are independent.
B) The events are not independent.
C) The events are mutually exclusive.
D) Not enough information is provided to determine the relationship.
Correct Answer: A
To check for independence, we must compare P(A and B) with P(A) * P(B). First, we find P(A and B) using the addition rule: P(A and B) = P(A) + P(B) - P(A or B) = 0.4 + 0.5 - 0.7 = 0.2. Next, we calculate the product of the individual probabilities: P(A) * P(B) = 0.4 * 0.5 = 0.2. Since P(A and B) = P(A) * P(B), the events are independent.
A) 0.25
B) 0.75
C) P(Y)
D) Cannot be determined without P(Y).
Correct Answer: A
The definition of independent events states that if X and Y are independent, knowing that Y has occurred does not change the probability of X. Therefore, P(X|Y) = P(X). Since P(X) = 0.25, P(X|Y) must also be 0.25.