Question

A and B are independent events. Which equation below must be true?

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

Answer 1

A and B are independent events. The equation below that must be true is P(A | B) = P(A). The answer is letter B. The rest of the choices do not answer the question above.

Answer 2

Answer: The correct option is (B) P(A | B) = P(A)

Step-by-step explanation: Given that A and B are independent events.

We are to select the TRUE statement from the given options.

We know that

if two events A and B are independent events, then the probability of the intersection of A and B is equal to the product of the probabilities of the events A and B.

That is,

`P(A\cap B)=P(A)* P(B).`

Now, the conditional probability of event A given that event B has already occured is given by

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

Thus, the correct statement is P(A | B) = P(A).

Option (B) is CORRECT.