In a certain town, 50% of the people own cats, 40% own dogs, and 10% don't own any pets. If someone in this town owns a cat, what is the probability they also own a dog?
Let's break down the information given:
1. We know that 50% of the people own cats.
2. We also know that 40% of the people own dogs.
3. And finally, we know that 10% of the people don't own any pets at all.

Now, let's consider the worst-case scenario for overlapping pet ownership: all the people who own cats also own dogs. This means that out of the 50% of cat owners, all of them would be part of the 40% dog owners as well. 

In this case, the probability of a cat owner also owning a dog would be 100%. However, since we don't have enough information about the actual overlap between cat and dog owners, we cannot determine the exact probability.

So, the answer is that we cannot determine the probability with the given information.