Part 2: Probability Suppose we have a sample space: S = {151, E2, E3, E4,E5,E6, E7}, with probabilities: P(El) = 0.05, P(Ez) = 0.20, P(Eg) = 0.20, P(E4) = 0.25, P(Es) = 0.15, Page) = 0.10, and P097) = 0.05. Consider the following events with their corresponding set of sample points: A = {131, E4, E6}, B = {E2,E4,E7}, and C = {E2,E3,E5,E7}. Note: 0 P(AUB) = P(A)+P(B) P(AnB) 0 PM U B) = P(A) + P(B) if A and B are mutually exclusive 0 P(A n B) = 0 if A and B are mutually exclusive 0 P(AC) = 1 P(A) . P(A I B) 2 P313?) 0 P(A | B) = P(A) iannd B are independent Questions: 7. Find the probabilities: P(A), P(B) and P(C). 8. Find the set of sample points of events A U B (this is a list of sample points {...}) and find P(A U B) ? 9. Find the set of sample points ofA n B and find P(A n B). 10. Now use the formula P(A U B) = P04) + P(B) P(A n B) to confirm your answer from part (b). 11. Are events A and C mutually exclusive? 12. Find 3' and P(BC) 13. Calculate PM | B) and P(B | A). Are they the same? 14. Are events A and B independent