Please help me understand this probability question ( Bayes)

Question

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 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 womans name was originally selected
from list 1?

 

We just finished learning Bayes Theorem so this question deals with that. My issue is with the formula. Im having a hard time figuring what probabilities to assign.

Answer 1

 

 

Baye's theorem says:

 

P ( woman from list 1  | given man selected) =

 

P ( man selected | woman from list 1) * P(woman from list 1) / P(man selected)

 

A woman from list 1 is added to list 2.

The probability of man from the augmented list of 3 women and 6 men is 6/9 = 2/3

 

Probability of woman from list 1 is 5/7.

Probability that man is selected 6/8  = 3/4

 

So  2/3 * 5/7 divided by 3/4 = 2/3 * 5/7 * 4/3 = 40/84 = 20/42 = 10/21