Question

Consider two events such that P(A)=3/4, P(B)=2/5 and P(AnB)=1/3. Are the events A and B independent?

Answer 1

If P(A) times P(B) is equal to P(A n B), then that shows the events are independent. Otherwise, they are dependent. When I write "A n B", I mean "A intersect B". The intersect symbol looks similar to the lowercase letter n.

P(A)*P(B) = (3/4)*(2/5) = (3*2)/(4*5) = 6/20 = 3/10

Since that result is not the same as P(A n B) = 1/3, this means that the events are not independent. They are dependent events. The answer is choice D