Question

If events A and B are independent, what must be true?A.) P(AB) = P(B)

Answer 1

Answer:

B.) P(A/B) = P(A)

Step-by-step explanation:

If two events, A and B are independent:

We have that:

$P(A \cap B) = P(A)P(B)$

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Since they are independent:

$P(A \cap B) = P(A)P(B)$

Then

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)$

So

$P(B|A) = P(B)$, or either:

$P(A|B) = P(A)$, and thus, the correct answer is given by option B.