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# Mutually Inclusive Events

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Practice Mutually Inclusive Events
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## Venn Diagrams

### Topic

Social Media and Venn Diagrams

### Vocabulary

• Venn Diagram
• Mutually Exclusive Events
• Mutually Inclusive Events
• Probability

### Student Exploration

#### How do you and your friends get connected with social media? And how could you represent their social media “likes” in a Venn diagram?

How can you represent your friends’ social media “likes” in a Venn diagram?

Today there are so many ways to connect and communicate with your friends online. You can comment on your friend’s most recent post on facebook, you can “like” a friend’s picture on instagram, you can retweet your friend’s post on twitter. How do you and your friends connect online? Survey ten of your friends or classmates on all the forms of social media that they use, record all the types. According to Wikipedia, Social media is web-based technologies that “turn communication into interactive dialogue among organization, communities, and individuals,” from http://en.wikipedia.org/wiki/Social_media. Below are some examples of popular forms of social media:

• hi5
• Friendster
• XING
• Plaxo
• Pinterest
• Instagram

After completing your survey of ten friends, examine the results of your survey and determine the three most popular forms of social media amongst your friends. Next, create a Venn diagram to represent the three forms of social that are most popular amongst your friends and who uses which type.

Sample Venn Diagram:

The following answers are based on the sample Venn diagram. Answers will vary, based on each Venn diagram.

1. Which of forms of social media are mutually exclusive? Remember that mutually exclusive events are events that cannot happen at the same time. Then write your answer in set notation. Twitter and Tumblr are mutually exclusive as none of the students use both forms of social media. Let $A = \text{Twitter}$ and $B = \text{Tumblr}$, $A\cup B = 0$.
2. Which of forms of social media are mutually inclusive?Remember that mutually inclusive events are events that occur at the same time. Then write your answer in set notation. None of the types of social media in the sample are mutually inclusive. If they were, the Venn Diagram would only include students in the parts of the circles that intersection, not in the other parts.
3. Take a picture of your Venn diagram, or scan it. Then upload it and share it with other CK-12 users! You can also use educreations.com to record your discussion of your Venn Diagram and then upload your video to the CK-12’s website!

### Extension Investigation

Let’s say that the first form of social media is “$A$”, the second form of social media is “$B$”, the third form of social media is “$C$”, and the fourth form of social media is “$D$.”

1. What is the probability that some from your survey uses social media $A$, $P(A)$? Let $A = \text{Twitter}$. Then $P(A) = \frac{4}{10} = \frac{2}{5}$ or 0.4 or 40%.
2. What is the probability that some from your survey uses social media $B$, $P(B)$? Let $B = \text{Tumblr}$. Then $P(B) = \frac{4}{10} = \frac{2}{5}$ or 0.4 or 40%.
3. What is the probability that some from your survey uses social media $C$, $P(C)$? Let $C = \text{Facebook}$. Then $P(C) = \frac{5}{10} = \frac{1}{2}$ or 0.5 or 50%.
4. What is the probability that some from your survey uses social media $D$, $P(D)$? Let $D = \text{Instagram}$. Then $P(D) = \frac{2}{10} = \frac{1}{5}$ or 0.2 or 20%.
5. Find $A \cup B$. Then find $P (A \cup B)$. $A \cup B = { }$. $P (A \cup B)= \frac{0}{10} = 0$.
6. Find $C \cup D$. Then find $P (C \cup D)$. $C \cup D = \{ \text{Joel}\}$.$P (C \cup D)=\frac{1}{10}$ or 0.1 or 10%.
7. Find $A \cap D$. Then find $P(A \cap D)$. $A \cap D = \{\text{Denise, Andrew, Ralph, Omar, Joel}\}$. $P(A \cap D) = \frac{5}{10}$.
8. Find $B \cap C$. Then find $P(B \cap C)$. $B \cap C =\{ \text{Ralph, Omar, Nida, Joel, Dave, Kristina, Tess, Cliff}\}$.$P(B \cap C)=\frac{8}{10}=\frac{4}{5}$ or 0.8 or 80%.
9. What is an example of an everyday event that is mutually exclusive? Explain. Yankee and Red Sox fans are mutually exclusive, as the two teams are rivals and (nearly) no one would be a fan of both teams.
10. What is an example of an everyday event that is mutually inclusive? Explain. Being an artist and being a strong right brain thinker. Visual thinking is described as using your right side of the brain and artists have strong right brain thinking skills. http://painting.about.com/od/rightleftbrain/a/Right_Brain.htm
11. Can a Venn diagram have more than four circles? Why or why not? Explain. Venn Diagram can have more than four circles but the intersecting parts of the circles become more difficult to distinguish. Creating a Venn diagram with four circles is useful only when there is a small amount of information to include in the intersecting parts of the circles.

### Connections to other CK-12 Subject Areas

• Venn Diagrams
• Probability of Compound Events
• Mutually Exclusive Events
• Mutually Inclusive Events
• Theoretical and Experimental Probability