1.1: Venn Diagrams
Suppose you have the set of integers from 1 to 19. How would you represent the set of odd numbers within that range and the set of prime numbers within that range? Can you think of an easy way to represent the union and intersection of those two different sets of numbers?
Watch This
First watch this video to learn about Venn diagrams.
CK12 Foundation: Chapter1VennDiagramsA
Then watch this video to see some examples.
CK12 Foundation: Chapter1VennDiagramsB
Watch this video for more help.
James Sousa Set Operations and Venn Diagrams  Part 2 of 2
Guidance
In probability, a Venn diagram is a graphic organizer that shows a visual representation for all possible outcomes of an experiment and the events of the experiment in ovals. Normally, in probability, the Venn diagram will be a box with overlapping ovals inside. Look at the diagram below:
The
Example A
2 coins are tossed one after the other. Event
We know that:
Notice that event
Example B
Event
We know that:
Notice that the overlapping oval for
In a Venn diagram, when events
Example C
You are asked to roll a die. Event
We know that:
Vocabulary
The possible results of 1 trial of a probability experiment are called outcomes, and the set of all possible outcomes of an event or group of events is the sample space. A Venn diagram is a diagram of overlapping circles that shows the relationships among members of different sets, and such a diagram helps us to find probability, or the chance that something will happen.
Guided Practice
Let’s say our sample space is the numbers from 1 to 10. Event
Answer:
We know that:
Notice that 3 of the prime numbers are part of both sets and are, therefore, in the overlapping part of the Venn diagram. The numbers 4, 6, 8, and 10 are the numbers not part of
Interactive Practice
Practice

ABC High School is debating whether or not to write a policy where all students must have uniforms and wear them during school hours. In a survey, 45% of the students wanted uniforms, 35% did not, and 10% said they did not mind a uniform and did not care if there was no uniform. Represent this information in a Venn diagram. 
ABC High School is debating whether or not to write a policy where all students must have uniforms and wear them during school hours. In a survey, 45% of the students wanted uniforms, and 55% did not. Represent this information in a Venn diagram.  For question 2, calculate the probability that a person selected at random from \begin{align*}ABC\end{align*} High School will want the school to have uniforms or will not want the school to have uniforms.
 Suppose \begin{align*}A=\{5, 6, 8, 10, 12\}\end{align*} and \begin{align*}B=\{8, 9, 12, 13, 14\}\end{align*}. What is \begin{align*}A \cup B\end{align*}?
 Suppose \begin{align*}A=\{1, 7, 13, 17, 21, 25\}\end{align*} and \begin{align*}B=\{7, 14, 21, 28, 35, 42\}\end{align*}. What is \begin{align*}A \cap B\end{align*}?
 In Jason's homeroom class, there are 11 students who have brown eyes, 5 students who are lefthanded, and 3 students who have brown eyes and are lefthanded. If there are a total of 26 students in Jason's homeroom class, how many of them neither have brown eyes nor are lefthanded?
 If event \begin{align*}A\end{align*} is randomly choosing a vowel from the letters of the alphabet, and event \begin{align*}B\end{align*} is randomly choosing a consonant from the letters of the alphabet, do the ovals in the Venn diagram that represents this situation overlap? Explain your answer.
 Use the following Venn diagram to answer the question:
 If the 2 ovals in the Venn diagram above represent events
 \begin{align*}A\end{align*}
 and
 \begin{align*}B\end{align*}
 , respectively, what is
 \begin{align*}A \cup B\end{align*}
 ?
 Use the following Venn diagram to answer the question:
 If the 2 ovals in the Venn diagram above represent events
 \begin{align*}A\end{align*}
 and
 \begin{align*}B\end{align*}
 , respectively, what is
 \begin{align*}A \cap B\end{align*}
 ?
 In the Venn diagram in question 9, what set represents event \begin{align*}A\end{align*}? What set represents event \begin{align*}B\end{align*}?
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Outcomes
The possible results of 1 trial of a probability experiment.probability
The chance that something will happen.Sample Space
In a probability experiment, the sample space is the set of all the possible outcomes of the experiment.Venn diagram
A diagram of overlapping circles that shows the relationships among members of different sets. Such a diagram helps us to find probability, or the chance that something will happen.Euler diagram
An Euler diagram is similar to a Venn diagram and is a visual representation of the relationship between sets, subsets, and members.Image Attributions
Here you'll learn how to draw a Venn diagram to represent the intersection and union of sets of numbers.