Consider independent events A and B.

a) Show that events A and Bc are also independent. (Justify intuitively for partial credit; prove rigorously for full credit.) Hint: One straightforward way is to show that P[Bc |A] = P[Bc ].
b) How about the events Ac and Bc ? (OK to assume part (a) even if you were not able to prove it).
c) Given known probabilities P[A] = pa and P[B] = pb, express the following probabilities: P[A â© B], P[A â© Bc ], and P[Ac â© Bc ]