A small city has three automobile dealerships: a GM dealer selling Chevrolets and Buicks; a Ford dealer selling Fords and Lincolns; and a Toyota dealer. If an experiment consists of observing the brand of the next car sold, then the events A = {Chevrolet, Buick) and B = (Ford, Lincoln} are mutually exclusive because the next car sold cannot be both a GM product and a Ford product (at least until the two companies merge!). (a) In the experiment, identify three events that are mutually exclusive. O A = (Toyota, Buick), B = (Buick, Ford), C = (Lincoln} O A = (Chevrolet, Toyota), B = (Buick, Ford), C= {Ford} O A = (Ford, Buick), B = (Chevrolet, Toyota), C = (Chevrolet) O A = {Chevrolet, Buick), B = (Ford, Lincoln), C = (Toyota} O A = {Chevrolet, Ford}, B = {Ford, Lincoln}, C = {Toyota) (b) Suppose there is no outcome common to all three of the events A, B, and C. Are these three events necessarily mutually exclusive? If your answer is yes, explain why; if your answer is no, give a counterexample using the experiment above. O No, the events A = {Chevrolet, Buick), B = (Buick, Ford), C = {Toyota)} are not mutually exclusive and there is no common outcome to all three events. O Yes, if there is no outcome common to all three events then the three events don't all overlap. So, the events must be mutually exclusive. O No, the events A = (Chevrolet, Buick), B = {(Ford, Lincoln), C = (Toyota} are not mutually exclusive and there is no common outcome to all three events. O No, the events A = {Chevrolet, Buick), B = {Buick, Ford), C = (Buick) are not mutually exclusive and there is no common outcome to all three events. O Yes, if there is no outcome common all three events then no outcome can be repeated in more than one event. So, the events must mutually exclusive.

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