A and B are independent events with no relation.

For example:

If a family have children (Event A) the chances the family has a dog also (Event C) is W.

if a family has a cat ( Event B) the chances the family has a dog too (Event C) is Z.

So if we have a family with children and a cat, Event A and Event B, what are the chances the family has a dog (Event C) ?

Is it W*Z the combination ? Is it Max(W,Z) not improving having both A and B? Is it W+Z improving the chances?

Thanks