Question

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

B.) P(A/B) = P(A)
C.) P(A) = P(B)
D.) OP(AB) = P(BIA)

Answer 1

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

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