I'd like to know where should I look for knowledge and patterns for this kind of problems.
Say we have two groups of people, A and B. We know that 80% of A group are males, while in B group only 30% are males. We also know that person x belongs to both groups. What are the changes that this person is a male?
My first thought was that we should count the average, but I realised that if we had 100% of males in A group, we obviously wouldn't count the average, so we should use some more sophisticated tools.
And the next question: how our estimation will change if we know how many people we have in A and B groups and how many of them belongs to both?
Unfortunately you can only do some actual estimation once you have the information you mentioned for your second question.