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)

3 and 6 are correct

Step-by-step explanation:

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

P(Y∩X)  = P(Y) * P(X)

We know that

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

Cancel out P(X)

So

Like that

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

Cancel out P(Y)

So

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

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation: