Q: A personal director has two lists of applicants for jobs. List 1 contains the names of five women and two men, whereas list 2 contains the names of two women and six men. A name is randomly selected from list 1 and added to list 2. A name is then randomly selected from the augmented list 2. Given that the name selected is that of a man, what is the probability that a woman's name was originally selected from list 1?
We just covered total probability and Baye's theorem. Even so, I am completely lost. I can't find any examples similar to this question. Some guidence would be appreciated.