By Ronald E Walpole; et al
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Example text
These new events will be subsets of the same sample space as the given events. Suppose that A and B are two events associated with an experiment. In other words, A and B are subsets of the same sample space S. For example, in the tossing of a die we might let A be the event that an even number occurs and B the event that a number greater than 3 shows. Then the subsets A = {2, 4, 6} and B = {4, 5, 6} are subsets of the same sample space S = {1, 2, 3, 4, 5, 6}. Note that both A and B will occur on a given toss if the outcome is an element of the subset {4, 6}, which is just the intersection of A and B.
Nk of a kth kind is n! n2 ! · · · nk ! 17: In a college football training session, the defensive coordinator needs to have 10 players standing in a row. Among these 10 players, there are 1 freshman, 2 sophomores, 4 juniors, and 3 seniors. How many different ways can they be arranged in a row if only their class level will be distinguished? 4, we find that the total number of arrangements is 10! = 12,600. 1! 2! 4! 3! Often we are concerned with the number of ways of partitioning a set of n objects into r subsets called cells.
Let Q be the event that the employee selected drinks alcoholic beverages. Then the event P ∪ Q is the set of all employees who either drink or smoke or do both. 14: If M = {x | 3 < x < 9} and N = {y | 5 < y < 12}, then M ∪ N = {z | 3 < z < 12}. The relationship between events and the corresponding sample space can be illustrated graphically by means of Venn diagrams. In a Venn diagram we let the sample space be a rectangle and represent events by circles drawn inside the rectangle. 5: Events represented by various regions.