If events A and B are independent, then which of the following is false?

A. P(A|B) = P(A)

B. P(B|A) = P(B)

C. P(B∣A) = P(A and B)/P(B)

D. P(A) * P(B) = P(A and B)

C. P(B∣A) = P(A and B)/P(B) is false

To see why...let P(A) = 0.2 and let P(B) = 0.4

Then

P(A and B) / P(B) = (0.2)(.0.4) / (0.4) = 0.2

But P(B IA) should be 0.4 if these are independent because A has no effect on B