(2) Given a sample space 2 and a probability measure P, two events A C and BCN are said to be independent if P(AB) = P(A)P(B). Assume that the events E1, E2 are independent. a) Prove that the events Ei, Es are also independent. b) If, in addition, P(E)= and P(E2) = 1, Prove that P(E UE) = 17 24 2 = c) Let E3 be a third event such that P(E3) 4, satisfying in addition that E and E3 are independent and also that E2 and E3 are independent. Prove that