2 lists PR a women select from first list given a man selected from second
A personnel 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 6 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 probabliity that a woman's name was originally selected from list 1?
This question is confusing me a little bit, but this is how I have done it;
with (That is, a man is selected from the second list, given a women select from first)
So the total probability of a man being selected from the second list is:
I am a little bit confused as to if I have calculated the probablities of the events happening, the 2 lists thing is confusing me a bit.. Thanks!