Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, ..., E7 denote the sample points. The following probability assignments apply: P(E1) = 0.10, P(E2) = 0.20, P(E3) = 0.10, P(E4) = 0.20, P(E5) = 0.10, P(E6) = 0.10, and P(E7) = 0.20. Assume the following events when answering the questions: A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7} a. Find P(A), P(B), and P(C). If necessary round your answers to two deicmal places. P(A) = P(B) = P(C) = b. What is A ∪ B? (i) {E3, E5} (ii) {E1, E2, E6, E7} (iii) {E1, E2, E4, E6, E7} (iv) {E1, E4, E6} (v) {E2, E4, E7} (vi) {∅} What is P(A ∪ B)? If necessary round your answer to two deicmal places. c. What is A ∩ B? (i) {E1, E2, E6, E7} (ii) {E4} (iii) {E1, E2, E3, E5, E6, E7} (iv) {E1, E4, E6} (v) {E2, E4, E7} (vi) {∅} What is P(A ∩ B)? If necessary round your answer to two deicmal places. d. Are events A and C mutually exclusive? e. What is Bc? (i) {E1, E3, E5, E6} (ii) {E2, E4, E5, E7} (iii) {E3, E4, E5, E6} (iv) {E1, E4, E6} (v) {E2, E4, E7} (vi) {∅} What is P(Bc)? If necessary round your answer to two deicmal places.