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# Mutually Inclusive Events

## Probability of two events that can occur at the same time P(A or B) = P(A) + P(B) -  P(A and B)

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Practice Mutually Inclusive Events

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Venn Diagrams
Teacher Contributed

## 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. You can make your Venn Diagram online at

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.
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.
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!

Connecting on social media.

### Extension Investigation

Let’s say that the first form of social media is “A\begin{align*}A\end{align*}”, the second form of social media is “B\begin{align*}B\end{align*}”, the third form of social media is “C\begin{align*}C\end{align*}”, and the fourth form of social media is “D\begin{align*}D\end{align*}.”

1. What is the probability that some from your survey uses social media A\begin{align*}A\end{align*}, P(A)\begin{align*}P(A)\end{align*}?
2. What is the probability that some from your survey uses social media B\begin{align*}B\end{align*}, P(B)\begin{align*}P(B)\end{align*}?
3. What is the probability that some from your survey uses social media C\begin{align*}C\end{align*}, P(C)\begin{align*}P(C)\end{align*}?
4. What is the probability that some from your survey uses social media D\begin{align*}D\end{align*}, P(D)\begin{align*}P(D)\end{align*}?
5. Find AB\begin{align*}A \cup B\end{align*}. Then find P(AB)\begin{align*}P (A \cup B)\end{align*}.
6. Find CD\begin{align*}C \cup D\end{align*}. Then find P(CD)\begin{align*}P (C \cup D)\end{align*}.
7. Find AD\begin{align*}A \cap D\end{align*}. Then find P(AD)\begin{align*}P(A \cap D)\end{align*}.
8. Find BC\begin{align*}B \cap C\end{align*}. Then find P(BC)\begin{align*}P(B \cap C)\end{align*}.
9. What is an example of an everyday event that is mutually exclusive? Explain.
10. What is an example of an everyday event that is mutually inclusive? Explain.
11. Can a Venn diagram have more than four circles? Why or why not? Explain

### Connections to other CK-12 Subject Areas

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

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