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The image shows a probability problem based on survey data that summarizes family size and car ownership. The data in the table is organized by three family size categories (1, 2 to 4, and over 4) and their corresponding car ownership (0 cars, 1 car, 2 or more cars).

Let's go over the questions and check the probabilities.

### Table Summary:
| Family Size | 0 Cars | 1 Car | 2 or More Cars | Total |
|-------------|--------|-------|----------------|-------|
| 1           | 11     | 9     | 2              | 22    |
| 2 to 4      | 5      | 14    | 7              | 26    |
| Over 4      | 13     | 9     | 9              | 31    |
| **Total**   | **29** | **32**| **18**         | **79**|

### Questions:

1. **What is the probability that the chosen respondent lives by themselves and owns 2 or more cars?**
   - "Lives by themselves" means family size = 1.
   - Look at the row for family size 1 and the column for 2 or more cars.
   - There are 2 people who live by themselves and own 2 or more cars.
   - Total respondents = 79.
   - Probability = \( \frac{2}{79} \).

   This is correct as shown in the image.

2. **What is the probability that the chosen respondent lives by themselves or owns 2 or more cars?**
   - We are looking for the union of the events: lives by themselves or owns 2 or more cars.
   - People who live by themselves: 22 people (family size 1).
   - People who own 2 or more cars: 18 people.
   - However, 2 people live by themselves *and* own 2 or more cars. We should not double-count them.
   - Therefore, total for this event = 22 + 18 - 2 = 38.
   - Probability = \( \frac{38}{79} \).

   This is correct.

3. **What is the probability that the chosen respondent lives by themselves?**
   - Total people who live by themselves = 22.
   - Total respondents = 79.
   - Probability = \( \frac{22}{79} \).

   This is correct.

4. **What is the probability that the chosen respondent owns no cars?**
   - Total people who own no cars = 29.
   - Total respondents = 79.
   - Probability = \( \frac{29}{79} \), but you entered \( \frac{11}{22} \), which is incorrect.

### Corrected Answer for Question 4:
The correct probability should be:
\[
\frac{29}{79}
\]

Let me know if you would like more details or have any questions!

### Relative Questions:
1. What is the probability that the chosen respondent lives in a family of 2 to 4 and owns exactly 1 car?
2. What is the probability that the chosen respondent owns 1 or more cars?
3. What is the probability that the chosen respondent lives in a family of over 4 and owns no cars?
4. How would you calculate the probability that a respondent either lives in a family of 2 to 4 or owns no cars?
5. What is the complement of the event "the chosen respondent lives by themselves"?

### Tip:
When calculating probabilities involving "or," remember to subtract the overlap to avoid double-counting!

A probability problem based on survey data that summarizes family size and car ownership. The data in the table is organized by family size categories and their corresponding car ownership.

Learn how to solve probability problems based on survey data that involves family size and car ownership. This detailed solution covers key concepts such as probability calculations and data analysis, suitable for students in Grades 9-12.

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