Question

If events X and Y are independent, what must be true? Check all that apply. P(Y | X) = 0 P(X | Y) = 0 P(Y | X) = P(Y) P(Y | X) = P(X) P(X | Y) = P(Y) P(X | Y) = P(X)

Answer 1

3 and 6 are correct

Explanation:

Answer 2

if events X and Y are independent, then for intersection we multiply the probability

P(Y∩X) = P(Y) * P(X)

We know that

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

Now we replace P(Y) * P(X) for P(Y∩X)

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

Cancel out P(X)

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

Like that

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

Now we replace P(X) * P(Y) for P(X∩Y)

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

Cancel out P(Y)

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

P(Y | X) = P(Y) and P(X | Y) = P(X) are true