Section 5-3 The Addition Rules for Probability

Union

A union of two events A and B, denoted by (AB) or by (A or B), is simply the set of all the outcomes in both A and B.

Example: If {1,2,3,4,5,6} and A={1,2,3} and B={2,4,6}, then (AB)={1,2,3,4,6}

Intersection

An intersection of two events A and B, denoted by (AB) or by (A and B), is the set of outcomes that A and B have in common.

Example:If {1,2,3,4,5,6} and A={1,2,3} and B={2,4,6}, then (AB)={2}

Another Definition

Disjoint events are events which have nothing in common, i.e., P(AB)=0

Addition Rule for Disjoint Events

If A and B are disjoint events, then P(A B)=P(A)+P(B)

The general addition rule

Previously, we found that P(AB)=P(A)+P(B) when A and B are disjoint. Now, we consider the case when A and B intersect. Hence, consider the following Venn diagram

Note that when we overlap the two circles, we obtain P(AB) twice. Hence,

P(AB)=P(A)+P(B)-P(AB)

Generated by GO manager: 2006-03-24