Question

If events X and Y are INDEPENDENT, then A) P(X|Y) = P(X) B) P(Y|X) = P(Y) C) P(X and Y) = P(X) x P(Y) D) A, B, and C are all correct

Answer 1

The correct option is D.

Explanation:

It is given that events X and Y are two independent events.

Two events are called independent events if the occurrence of one does not affect the probability other. It means

`P(X\text{ and }Y)=P(X)\cdot P(Y)`

`P(X\cap Y)=P(X)\cdot P(Y)` ..... (1)

Therefore option C is correct.

We know that

`P(X|Y)=(P(X\cap Y))/(P(Y))`

Using equation (1),

`P(X|Y)=(P(X)\cdot P(Y))/(P(Y))`

`P(X|Y)=P(X)`

Therefore option A is correct.

We know that

`P(Y|X)=(P(X\cap Y))/(P(X))`

Using equation (1),

`P(Y|X)=(P(X)\cdot P(Y))/(P(X))`

`P(Y|X)=P(Y)`

Therefore option C is correct.

Since options A, B and C are correct, therefore we can say that correct option is D.