Combining events

Summary

Creating new events

Given two events \(A\) and \(B\) , we can create new events.

• \(A∪B\) ("A union B") is an event which is true only if either \(A\) is true or \(B\) is true (or both)
• \(A∩B\) (A intersection B) is an event which is true only if \(A\) is true and \(B\) is true
• \(A^C\) (A complement) is an event which is true only if \(A\) is false.

Example

• \(S={1,2,3,4,5,6}\) and \(A={1,2,3}\) , \(B={2,3,4}\) are two events . We then have \(A∪B={1,2,3,4},A∩B={2,3}\) and \(A^C={4,5,6}\) .

Example

• \(A\) and \(B\) are mutually exclusive events if and only if \(A∩B=∅\) .