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

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

P(Y∩X)  = P(Y) * P(X)

We know that

$P(Y|X) =\frac{P(YintersectionX)}{P(X)}$

Now we replace P(Y) * P(X) for  P(Y∩X)

$P(Y|X) =\frac{P(Y)*P(X)}{P(X)}$

Cancel out P(X)

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

Like that

$P(X|Y) =\frac{P(XintersectionY)}{P(Y)}$

Now we replace P(X) * P(Y) for  P(X∩Y)

$P(X|Y) =\frac{P(X)*P(Y)}{P(Y)}$

Cancel out P(Y)

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

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

Answer 2

Answer:

3 and 6 are correct

Step-by-step explanation: