**Problem 4: Using the provided data, describe the set $ U \cap E' $ in words, and calculate the number of elements it contains.**The table displays data on the success of new and established authors:| | New Authors | Established Authors | Total ||----------------------|-------------|---------------------|-------|| **Successful** | 5 | 25 | 30 || **Unsuccessful** | 15 | 55 | 70 || **Total** | 20 | 80 | 100 |**Explanation:**- **Rows:** - The first row indicates the number of successful authors, with new authors having 5 and established authors 25, totaling 30 successful authors. - The second row indicates the number of unsuccessful authors, showing that new authors are 15 and established authors 55, making a total of 70 unsuccessful authors. - **Columns:** - The first column shows details for new authors, with a total of 20. - The second column is for established authors, totaling 80. - The last column provides the total for each category, adding up to 100 authors in total.**Set $ U \cap E' $** refers to the intersection of unsuccessful authors (U) and new authors (E'). This is represented by the category "Unsuccessful New Authors" in the table, which is 15.Therefore, the set $ U \cap E' $ contains 15 elements.

Given, The contingency table. U be the Unsuccessful S be the successful And E be the established…

Answered: 4. Using the table below, describe the…

4. Using the table below, describe the set U N E' in words, and find the number of elements it contains. New Authors Established Authors Total Successful 25 30 Unsuccessful 15 55 70 Total 20 80 100

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

**Problem 4: Using the provided data, describe the set $ U \cap E' $ in words, and calculate the number of elements it contains.**

The table displays data on the success of new and established authors:

| | New Authors | Established Authors | Total |
|----------------------|-------------|---------------------|-------|
| **Successful** | 5 | 25 | 30 |
| **Unsuccessful** | 15 | 55 | 70 |
| **Total** | 20 | 80 | 100 |

**Explanation:**

- **Rows:**
- The first row indicates the number of successful authors, with new authors having 5 and established authors 25, totaling 30 successful authors.
- The second row indicates the number of unsuccessful authors, showing that new authors are 15 and established authors 55, making a total of 70 unsuccessful authors.

- **Columns:**
- The first column shows details for new authors, with a total of 20.
- The second column is for established authors, totaling 80.
- The last column provides the total for each category, adding up to 100 authors in total.

**Set $ U \cap E' $** refers to the intersection of unsuccessful authors (U) and new authors (E'). This is represented by the category "Unsuccessful New Authors" in the table, which is 15.

Therefore, the set $ U \cap E' $ contains 15 elements.

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