CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 3. An Introduction to Probability

2. EventDcorresponds to finding the simple eventS(D) =D={ 5 }. So

A∩D={ 2 , 4 , 6 }∩{ 5 }

=φ

Whereφis the empty set. This says that there are no elements in the setA∩D. This means that you will not observe

any events that combine setsAandD.

3. Here, we need to be a little careful. We need to find the intersection of three sets. To do so, it is a good idea to use
   the associativity property by finding first the intersection of setsAandBand then intersecting the resulting set with
   C. Here is how:

(A∩B)∩C= ({ 2 , 4 , 6 }∩{ 1 , 2 , 3 })∩{ 6 }

({ 2 }∩{ 6 })

=φ

Again, we get the empty set.

Lesson Summary

1. Theunionof two eventsAandB,A∪B, occurs if either eventAor eventBor both occur on a single
   performance of an experiment. A union is an"or" relationship.


2. Theintersectionof two eventsAandB,A∩B, occurs only if both eventAand eventBoccur on a single
   performance of an experiment. An intersection is an"and" relationship.


3. Intersections and unions can be used to combine more than two events.