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Chapter 4: Problem 66

Explain the meaning of the union of two events. Give one example.

Short Answer

Expert verified
The union of two events, A and B, is an event that includes all the outcomes from either event A, event B, or both. For instance, if tossing a die represents the sample space, and A is the event of getting an even number while B is the event of getting a number less than 4; the union of A and B represents the event of getting either an even number or a number less than 4.

Step by step solution

01

Definition of Union of Two Events

In probability theory, the union of two events A and B (denoted as \(A \cup B\)) refers to the event that either event A, event B, or both occur. So, if we have two events within a sample space, the union of these two events includes all outcomes that belong to either one of these two events or to both.
02

Explanation of the Concept using an Example

Let's take a practical example. Suppose we are tossing a die and let event A be the event that the die shows an even number (i.e., A = {2, 4, 6}) and let event B be the event that the die shows a number less than 4 (i.e., B = {1, 2, 3}). The union of these two events, \(A \cup B\), would be the event that the die shows either an even number or a number less than 4, so \(A \cup B\) = {1, 2, 3, 4, 6}.

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