Question

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

Answer 1

If an event is independent, it means other events have no effect on this event.

So this means P(A | B) = P(A) because A and B are independence thus event B does not change anything regarding event A.

Hope this helps.

Answer 2

Answer:

The condition P(A|B) = x is true.

Step-by-step explanation:

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

If the two events are independent.

To find : Which condition must be true?  

Solution :

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

If two events are independent

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

The formulas for conditional probabilities are

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

If we substitute the independent condition in conditional probability formulas we get,

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

Applying the given condition,

$P(A/B)=P(A)=x\\\\P(B/A)=P(B)=y$

Therefore, The condition P(A|B) = x is true.