2) Given a sample space and a probability measure P, two events A and B 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 E1c,E2c are also independent. b) If, in addition, P(E1)=21 and P(E2)=31, Prove that P(E1E2)=32. c) Let E3 be a third event such that P(E3)=41, satisfying in addition that E1 and E3 are independent and also that E2 and E3 are independent. Prove that 2417P(E1E2E3)2419