Contingency Tables and Conditional Probability: Homework and Passing a Course A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below. Passed the Course Did not Pass the Course Total Completed HW Did not Complete HW 27 8 6 33 16 24 Total 35 22 57 A student from the class is randomly selected. Determine the following probabilities. Enter your results as percents rounded to two decimal places. What is the probability a student completed the HW? What is the probability a student passed the course and did not complete the HW? What is the probability a student did not pass the course or completed the HW? What is the probability a student passed the course given that they completed the HW?

Contingency Tables and Conditional Probability: Homework and Passing a Course A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below. Passed the Course Did not Pass the Course Total Completed HW Did not Complete HW 27 8 6 33 16 24 Total 35 22 57 A student from the class is randomly selected. Determine the following probabilities. Enter your results as percents rounded to two decimal places. What is the probability a student completed the HW? What is the probability a student passed the course and did not complete the HW? What is the probability a student did not pass the course or completed the HW? What is the probability a student passed the course given that they completed the HW?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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**Contingency Tables and Conditional Probability: Homework and Passing a Course**

**Overview:**
A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are summarized in the table below.

**Table:**

| | Completed HW | Did not Complete HW | Total |
|------------------------------|--------------|---------------------|-------|
| **Passed the Course** | 27 | 8 | 35 |
| **Did not Pass the Course** | 6 | 16 | 22 |
| **Total** | 33 | 24 | 57 |

**Questions:**

A student from the class is randomly selected. Determine the following probabilities. Enter your results as percents rounded to two decimal places.

1. **What is the probability a student completed the HW?**
- \[ \phantom{0000} \] %

2. **What is the probability a student passed the course and did not complete the HW?**
- \[ \phantom{0000} \] %

3. **What is the probability a student did not pass the course or completed the HW?**
- \[ \phantom{0000} \] %

4. **What is the probability a student passed the course given that they completed the HW?**
- \[ \phantom{0000} \] %

**Explanation of the Table:**
- The table is a contingency table displaying the relationship between two variables: homework completion and passing the course.
- Rows represent whether students passed or did not pass the course.
- Columns represent whether students completed or did not complete their homework.
- Each cell count represents the number of students falling into each category.
- The total row at the bottom and the total column on the right sum the number of students in each category respectively.

**Graphical/Diagram Explanation:**
The table provided is a standard contingency table used to showcase the distribution of student outcomes based on two categorical variables: homework completion and passing the course. There are no additional graphs or diagrams associated with this table.

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