I hope this is the right board for this.

In my statistical math class, we have homework assignments online. As I was doing the homework I ran into one problem I couldn't wrap my head around. It's the generic dogs and cats community one with different numbers.

Statement: In a certain community, 20% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 30% of all the families own a cat.

First Q:
What is the probability that a randomly selected family owns a cat?
Easy enough, .3.

Second Q:
What is the conditional probability that a randomly selected family owns a dog diven that it doesn't own a cat?

I won't get into details, but I tried and tried on this question and in the end I didn't get it. The answer came out to be 0.228571428571429. I just can't see how this came about. I tried following the conditional probablity forumla, P(A|B) = P(AnB)/P(B), but nothing led to the answer. Is there some abstract way I have to think about this?

If you're going to ask why I don't ask the professor, please just don't.