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Please help me understand this probability question ( Bayes)

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.
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1 Answer

 
 
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
 
 

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