a. In Example 2.10, identify three events that are mutually exclusive. b. Suppose there...

a. In Example 2.10, identify three events that are mutually exclusive.

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 of Example 2.10.

Reference example 2.10

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!). The operations of union and intersection can be extended to more than two events. For any three events A, B, and C, the event A ∪B & ∪C is the set of outcomes contained in at least one of the three events, whereas A ´ ∩B ´ ∩C is the set of outcomes contained in all three events. Given events A₁,A₂,A₃,…….., these events are said to be mutually exclusive (or pairwise disjoint) if no two events have any outcomes in common.

A pictorial representation of events and manipulations with events is obtained by using Venn diagrams. To construct a Venn diagram, draw a rectangle whose interior will represent the sample space . Figure 2.1 shows examples of Venn diagrams.