# Math Help - 2 lists PR a women select from first list given a man selected from second

1. ## 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;
$P(W|M)= \frac{P(W) \cdot P(M|W)}{P(M)}$

with $P(M|W) = \frac{6}{9}$ (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: $P(M)=P(W)\cdot P(M|W)+P(\bar{W}) \cdot P(M| \bar{W})=\frac{5}{7} \cdot \frac{6}{9} + \frac{2}{7} \cdot \frac{7}{9}=0.698413$

So
$P(W|M)=\frac{\frac{5}{7}\cdot \frac{6}{9}}{0.698413}=.69843$

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!

2. Hello,

Looks great Though your last result is wrong, you may have mistyped something in your calculator...
If the two lists confuse you, you could've named the events given they happen with the first or second list, like $W_1, M_2$
But this was not important since you defined well the events

3. Ah, Thanks Moo!
I think 0.6818 is more like it? I just recently got a TI-89 and still getting use to it

4. Originally Posted by Robb
Ah, Thanks Moo!
I think 0.6818 is more like it? I just recently got a TI-89 and still getting use to it

5. Originally Posted by Robb
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;
$P(W|M)= \frac{P(W) \cdot P(M|W)}{P(M)}$

with $P(M|W) = \frac{6}{9}$ (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: $P(M)=P(W)\cdot P(M|W)+P(\bar{W}) \cdot P(M| \bar{W})=\frac{5}{7} \cdot \frac{6}{9} + \frac{2}{7} \cdot \frac{7}{9}=0.698413$

So
$P(W|M)=\frac{\frac{5}{7}\cdot \frac{6}{9}}{0.698413}=.69843$

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!