Let's solve the problem by following these steps:

We need to determine the probability that, for two people selected at random without replacement (WR), both are cat owners.

1. Find Total People:

The table provides the number of people who own cats, dogs, and other pets, separated by age group. We must first calculate the total number of people.

• Over 40: $100 + 50 + 30 = 180$
• 40 or Under: $50 + 50 + 20 = 120$

Thus, the total number of people is $180 + 120 = 300$.

2. Find Total Cat Owners:

Next, we calculate the total number of cat owners across all age groups:

• $100$ people over 40 own cats.
• $50$ people 40 or under own cats.

Thus, the total number of cat owners is $100 + 50 = 150$.

3. Probability of Selecting Two Cat Owners:

We are asked to find the probability that two people selected at random are both cat owners.

The probability of selecting one cat owner on the first draw is: $P(\text{First Cat Owner}) = \frac{150}{300} = 0.5$

Once the first person has been selected, there are 149 cat owners left out of 299 people. So the probability that the second person is also a cat owner is: $P(\text{Second Cat Owner | First Cat Owner}) = \frac{149}{299}$

4. Final Probability:

The probability of both people being cat owners is the product of these two probabilities: $P(\text{Both Cat Owners}) = P(\text{First Cat Owner}) \times P(\text{Second Cat Owner | First Cat Owner}) = 0.5 \times \frac{149}{299}$

Let me calculate this value for you.The probability that both people selected at random are cat owners is approximately 0.2492 (to four decimal places).

Would you like further explanation on any part of the solution, or do you have any questions? Here are some related questions to explore:

1. What is the probability of selecting two dog owners instead of cat owners?
2. How would the probability change if the selection was done with replacement?
3. What is the probability that the first person selected is a dog owner and the second is a cat owner?
4. How would the probabilities change if we focused only on people over 40?
5. What is the probability that at least one of the two selected people is a cat owner?

Tip: When dealing with probabilities in cases where selections are made without replacement, always adjust the total number of possible outcomes after each selection.