http://www.ck12.org Chapter 1. Independent and Dependent Events
CHAPTER
(^1) Independent and
Dependent Events
Chapter Outline
1.1 Venn Diagrams
1.2 INDEPENDENTEVENTS ANDSAMPLESPACES
1.3 DEPENDENTEVENTS ANDSAMPLESPACES
1.4 MUTUALLYEXCLUSIVEEVENTS
1.5 MUTUALLYINCLUSIVEEVENTS
Introduction
Probability is present in many parts of our everyday lives. When you say it is raining and your numbers came up in
the lottery, you are talking about 2 independent events. The fact that it is raining is not dependent on the fact that
your numbers came up in the lottery, and vice versa. If you say that you have the flu and you are taking medicine,
you are talking about dependent events. The terms independent and dependent in mathematics are the same as
those found in the English language. In order to determine probabilities mathematically, we need to understand the
differences between the definitions of independent and dependent. Independent events are those where the outcome
of one event is not affected by the other, and dependent events are events where the outcome of one is affected
by the other. Other terms, such as mutually inclusive and mutually exclusive, are also important. With mutually
inclusive events, the concept of double counting is taken into account in the calculation of probabilities when using
the Addition Principle.