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:

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!