http://www.ck12.org Chapter 3. An Introduction to Probability
3.2 Compound Events
Learning Objectives
- Know basic operations of unions and intersections.
- Calculate the probability of occurrence of two (or more) simultaneous events.
- Calculate the probability of occurrence of either of the two (or more) events.
Union and Intersection
Sometimes, we need to combine two or more events into one compound event. This compound event can be formed
in two ways.
Definition
Theunionof two eventsAandBoccurs if either eventAor eventBor both occur on a single performance
of an experiment. We denote the union of the two events by the symbolA∪B. You can say this symbol with
either “AunionB” or “AorB”.
The word “or” is used withunion:
A∪Bmeans everything that is in setAORin setBORin both sets.Definition
Theintersectionof two eventsAandBoccurs if both eventAand eventBoccur on a single performance of
an experiment. We denote the intersection of two events by the symbolA∩B. The most common way to say
this symbol is “AandB”.
The word “and” is used withintersection:
A∩Bmeans everything that is in setAANDin setB.Example:
Consider the throw of a die experiment. Assume we define the following events:
A:{observe an even number}
B:{observe a number less than or equal to 3}- DescribeA∪Bfor this experiment.
- DescribeB∩Bfor this experiment.
- CalculateP(A∪B)andP(A∩B), assuming the die is fair.
Solution:
The sample space of a fair die isS={ 1 , 2 , 3 , 4 , 5 , 6 }. The sample spaces of the eventsAandBabove areS(A) =A=
{ 2 , 4 , 6 }andS(B) =B={ 1 , 2 , 3 }.