1.1. Venn Diagrams http://www.ck12.org
Notice that the overlapping oval forAandBrepresents the students who have a part-time job and are on the honor
roll. The sample space,S, outside the ovals represents students neither holding a part-time job nor on the honor roll.
In a Venn diagram, when eventsAandBoccur, the symbol used is∩. Therefore,A∩Bis the intersection of events
AandBand can be used to find the probability of both events occurring. If, in a Venn diagram, eitherAorBoccurs,
the symbol is∪. This symbol would represent the union of eventsAandB, where the outcome would be in eitherA
orB.
Example C
You are asked to roll a die. EventAis the event of rolling a 1, 2, or a 3. EventBis the event of rolling a 3, 4, or a 5.
Draw a Venn diagram to represent this example. What isA∩B? What isA∪B?
We know that:
S={ 1 , 2 , 3 , 4 , 5 , 6 }
A={ 1 , 2 , 3 }
B={ 3 , 4 , 5 }
A∩B={ 3 }
A∪B={ 1 , 2 , 3 , 4 , 5 }
Guided Practice
Let’s say our sample space is the numbers from 1 to 10. EventAis randomly choosing one of the odd numbers from
1 to 10, and eventBis randomly choosing one of the prime numbers from 1 to 10. Remember that a prime number
is a number whose only factors are 1 and itself. Draw a Venn diagram to represent this example. What isA∩B?
What isA∪B?
Answer: