2. Let there be a set of sample points E, E2,..., Es, such that P(E) =...

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2. Let there be a set of sample points E₁, E2,..., Es, such that P(E₁) = 0.12 P(E2) = 0.06 P(E3) = 0.15 P(E5) = 0.05 P(E6) = 0.28 P(E7) = 0.07 P(E4) = 0.15 P(E8) = 0.12 and let use define the event that A = {E1, E2, E4, E5, E7} and B = {E2, E3, E4, E5, E6}. Find the following probabilities: a. P(AC) b. P(BC) c. P(ACB) d. P(A U B) e. P(ANB) f. P(ACN BC) g. P(AC U BC) h. Are the events A and B mutually exclusive? Why? 2. Let there be a set of sample points E₁, E2,..., Es, such that P(E₁) = 0.12 P(E2) = 0.06 P(E3) = 0.15 P(E5) = 0.05 P(E6) = 0.28 P(E7) = 0.07 P(E4) = 0.15 P(E8) = 0.12 and let use define the event that A = {E1, E2, E4, E5, E7} and B = {E2, E3, E4, E5, E6}. Find the following probabilities: a. P(AC) b. P(BC) c. P(ACB) d. P(A U B) e. P(ANB) f. P(ACN BC) g. P(AC U BC) h. Are the events A and B mutually exclusive? Why?