Question

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?

A. P(B|A) = y
B. P(A|B) = y
C. P(B|A) = x
D. P(A and B) = x + y
P(A and B) = x

P(A) y

Answer 1

The answer is A. P(B|A)=y

Answer 2

The correct options are:

A. P(B|A) = y

Explanation:

We know that when two events A and B are independent.

Then,

P(A∩B)=P(A)×P(B)

As we are given:

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

Hence,

P(A∩B)=xy

Also,

`P(A|B)=(P(A\bigcap B))/(P(B))\\\\\\P(A|B)=(P(A)* P(B))/(P(B))\\\\\\P(A|B)=P(A)`

Hence, P(A|B)=x

and similarly,

`P(B|A)=(P(A\bigcap B))/(P(A))\\\\\\P(B|A)=(P(A)* P(B))/(P(A))\\\\\\P(B|A)=P(B)`

Hence,

P(B|A)=y