**Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning.****Click the icon to view the Venn diagram.**---**Explanation:**The events **are not** mutually exclusive, since there **is at least 1 presidential candidate who lost the state of Montana and lost the election.**---**Detailed Analysis of the Venn Diagram:**The Venn diagram illustrates the relationship between two events within the sample space of presidential candidates. The two sets are defined as follows:1. **Presidential candidates who lost the state of Montana** (represented by the blue circle).2. **Presidential candidates who lost the election** (represented by the pink circle).The diagram indicates an intersection between the two sets (the overlapping region), showing that there exists at least one candidate who falls into both categories:- These are the presidential candidates who lost the state of Montana and also lost the overall election.Since there is an intersection, the events are not mutually exclusive.

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Answered: Decide whether the events shown in the…

Math

Statistics

Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 13CYU

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Question

100%

**Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning.**

**Click the icon to view the Venn diagram.**

---

**Explanation:**
The events **are not** mutually exclusive, since there **is at least 1 presidential candidate who lost the state of Montana and lost the election.**

---

**Detailed Analysis of the Venn Diagram:**

The Venn diagram illustrates the relationship between two events within the sample space of presidential candidates. The two sets are defined as follows:

1. **Presidential candidates who lost the state of Montana** (represented by the blue circle).
2. **Presidential candidates who lost the election** (represented by the pink circle).

The diagram indicates an intersection between the two sets (the overlapping region), showing that there exists at least one candidate who falls into both categories:
- These are the presidential candidates who lost the state of Montana and also lost the overall election.

Since there is an intersection, the events are not mutually exclusive.

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