To find the probability that a randomly selected person owns both a pet and a car, we use the information provided in the problem.

Solution

1. Total number of people surveyed: $N = 500$.

2. Number of pet owners who also own a car: 100.

3. To determine the probability that a randomly selected person owns both a pet and a car, we calculate: $P(\text{owns a pet and a car}) = \frac{\text{Number of people who own both a pet and a car}}{\text{Total number of people surveyed}}$

4. Substituting the values: $P(\text{owns a pet and a car}) = \frac{100}{500} = 0.2$

Answer

The probability that a randomly selected person owns both a pet and a car is 0.2, or 20%.

Would you like further details or have additional questions?

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Here are some related questions to deepen your understanding:

1. What is the probability that a randomly selected person owns a car, regardless of pet ownership?
2. What is the probability that a randomly selected person owns only a pet but not a car?
3. If a person is known not to own a car, what is the probability that they own a pet?
4. How would the probability change if the total number of pet owners was different?
5. What is the probability that a randomly selected person owns neither a pet nor a car?

Tip: When calculating joint probabilities, always ensure you know the total number of events in your population to determine accuracy.