Question

Which statement implies that A and B are independent events?

A. P(B | A) = P(B ∩ A)
B. P(B ∪ A) = P(B)
C. P(B ∩ A) = P(A)
D. P(B | A) = P(B)

Answer 1

The statement that implies that A and B are independent events is option D, P(B | A) = P(B).

Step-by-step explanation:

In this question, the statement that implies that A and B are independent events is option D, P(B | A) = P(B).

To determine if two events are independent, we can check if the probability of event B given event A is equal to the probability of event B occurring. If these probabilities are equal, then the events are independent.

For example, if we flip a fair coin twice, event A can be getting heads on the first flip and event B can be getting tails on the second flip. The probability of getting tails on the second flip, given that we got heads on the first flip, is 0.5 (since the outcomes of the coin flips are independent). This probability is equal to the probability of getting tails on the second flip, regardless of the outcome of the first flip. Therefore, event A and event B are independent.