Listed below are the types and ages of four monkeys procured by a laboratory for a drug trial.

Suppose two monkeys will be selected by lottery and assigned to an experimental drug. Considering all possible choices of two monkeys, make a Venn digram and show the following events.

Here the elementary outcomes are the possible choices of a pair of numbers from . These pairs are listed and labeled as e1,e2,e3,e4,e5,e6for ease of reference.

The pair hasboth monkeys of the same type, and so does the pair . Consequently, . Those with the same ages are , , and , so . And the diagram.

Refer to the previous experiment of selectng two monkeys out of four. Let , , , Give the compositions of the events

The pairs consisting of different types are , , , and , so . The event is the same as the event C. Employing the definitions of union and intersection, we obtain