AP Statistics 4.6 Independent Events and Unions of Events- MCQs - Exam Style Questions

Two events, A and B, are independent if the probability that they both occur is equal to the product of their individual probabilities. The rule is: $P(A \text{ and } B) = P(A) \times P(B)$.

Let’s find the probabilities from the table:
–   $P(A)$ = Probability that Question 1 is correct. We add the probabilities in the “Correct” column for Question 1: $0.25 + 0.08 = 0.33$.
–   $P(B)$ = Probability that Question 2 is correct. We add the probabilities in the “Correct” row for Question 2: $0.25 + 0.20 = 0.45$.
–   $P(A \text{ and } B)$ = Probability that both are correct. This is given directly in the table: $0.25$.

Now, let’s check if the independence rule holds:
Is $P(A) \times P(B) = P(A \text{ and } B)$?
$0.33 \times 0.45 = 0.1485$

Since $0.1485$ is not equal to $0.25$, the events are not independent. Option (C) correctly states this reasoning.
✅ Answer: (C)