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. Identify three events that are mutually exclusive.
1. A = {Ford, Buick), B = {Chevrolet, Toyota), C = {Chevrolet).
2. A = (Chevrolet, Buick), B Ford, Lincoln, C= (Toyota).
3. A-(Chevrolet, Ford), B-(Ford, Lincoln), C-(Toyota).
4. A = (Toyota, Buick), B- [Buick, Fordł, C = (Lincoln).
5. A = (Chevrolet, Toyota), B (Buick, Ford), C= (Ford).
B. Suppose there is no outcome common to all three of the events A, B, and C. Are these three events necessarily mutually exclusive?
1. No, the events A = {Chevrolet, Buck), B (Buick, Ford), C = {Buick) are not mutually exclusive and there is no common outcome to a three events.
2. 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.
3. Yes, if there is no outcome common to three events then the three events don't all overlap. So, the events must be mutually exclusive.
4. 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.
5. Yes, if there is no outcome common to all three events then no outcome can be repeated in more than one event. So, the events must be mutually exclusive.