Robin purchased shares of a machine tool company and shares of an airline company. Let E be the event that the shares of the machine tool company increase in value over the next 5 months, and let F be the event that the shares of the airline company increase in value over the next 5 months. Using the symbols ∪, ∩ and ^c describe the event that the shares of only one of the two companies increase in value. A) (E ∩ F^c) ∪ (E^c ∩ F) B) E ∪ F C) E^c ∩ F^c D) Ø

Question

Quizplus · Accepted Answer

The event that the shares of only one of the two companies increase in value can occur in one of the two ways: either the shares of the machine tool company increase in value, while the shares of the airline company do not increase in value, or the shares of the airline company increase in value, while the shares of the machine tool company do not increase in value. Therefore, this event can be described as the union of two disjoint events: (E ∩ F' ) and (E' ∩ F). Using set notation, this can be expressed as (E ∩ F^c) ∪ (E^c ∩ F).

Robin Purchased Shares of a Machine Tool Company and Shares