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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

User Jwok
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5 votes

Answer:

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.

User Neutron Stein
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