One More Probability Question

Many skipped classes: GPA < 2 = 80 people, GPA between 2 and 3 = 25 people, GPA > 3 = 5 people

Few skipped classes: GPA < 2 = 175 people, GPA between 2 and 3 = 450 people, GPA > 3 = 265

Are "GPA between 2 and 3" and "skipped few classes" independent?

A. No, b/c .475 does not equal .506

B. No, b/c .475 does not equal .89

C. No, b/c .450 does not equal .475

D. Yes, because of conditional probabilities

E. Yes, because of the product rule

I know that they are independent if P(A n B) = P(A) * P(B)

.45 = .475 * .89

No it does not, .45 does not equal .42275

Re: One More Probability Question

For independence we need : P(A|B) = P(A)

P("GPA between 2 and 3" |"skipped few classes") =450/890=0.506

P("GPA between 2 and 3") = 0.475

A) No, b/c .475 does not equal .506