Question

The probability of event A is x, and the probaility of event B is y.

If the two events are independent, which condition must be true?
P(A|B) = x
P(A|B) = y
P(B|A) = x
P(B|A) = xy

Answer 1

Answer: The correct option is (A) P(A\B) = x.

Explanation: Given that the probability of event A is x, and the probability of event B is y.

We are to select the correct condition that must be true if the two events A and B are independent.

According to the given information, we have

P(A) = x and P(B) = y.

We know that if two events A and B are independent, then

P(A\B) = P(A) and P(B\A) = P(B).

Therefore,

P(A\B) = P(A) = x,

⇒ P(A\B) = x.

Thus, option (A) is correct.

Answer 2

P(A)=x
P(B)=y

If the two events are independent:
P(A|B)=P(A)→P(A|B)=x
P(B|A)=P(B)→P(B|A)=y

Answer: First option P(A|B)=x