SOLUTION: The table shows the number of employed and unemployed workers in the United States in thousands in 2000. Assume that one person will be randomly selected from the group described i

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Question 478970: The table shows the number of employed and unemployed workers in the United States in thousands in 2000. Assume that one person will be randomly selected from the group described in the table. Find the probability of selecting a person who is employed given that the person is male.
In the table are these #'s under these headings from Left to Right.
Employed******/*********Unemployed
Male 67761*********/*********2433
Female 58655*********/*********2285
I have tried dividing only the males who are employed by the unemployed males but do not know if that is correct or not. Thank you for your time.
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The table shows th number of employed and unemployed workers in the United States in thousands in 2000. Assume that on e person will be randomly selected from the group described in the table.
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Find the probability of selecting a person who is employed given that the person is male.
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Note: The "Given" condition becomes your universe.
So you only look for the number of employed on the "male" line.
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In the table are these #'s under these headings from Left to Right.
Employed******/*********Unemployed
Male 67761*********/*********2433
Female 58655*********/*********2285
I have tried dividing only the males who are employed by the unemployed males but do not know if that is correct or not.
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Ans: 67761/(67761+2433) = 0.9653
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Cheers,
Stan H.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your table is as follows if i understand it correctly:

employed unemployed male 67761 2433 female 58655 2285

the question is:
find the probability of selecting a person who is employed, given that the person is male.
if you are given that the person is male, then the probability of getting an employed male is the number of employed males divided by the total number of males.
that would be:

the probability of getting an employed male is .965338918.
this is because .965338918 * the total number of males is employed.
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there is a formula that says that:
p(e|m) =
this formula states:
the probability of e given m is equal to the probability of (e intersect m) divided by the probability of m.
e is employed
m is male.
this formula will also give you the same answer, but the numbers are derived as follows:

employed unemployed total male 67761 2433 70164 female 58655 2285 60940 total 126416 4718 131134

p(e and m) is equal to
p(m) is equal to
p(e|m) =
it's exactly the same as we derived above.
in the first way we figured it out, our universe became only the men.
in the second way we figured it out, our universe was everybody.
the formulas give you the same number.
the first method was which was the number of employed males divided by the total number of males.
the second method was:

becomes which is equivalent to:
which is equivalent to:

the 131134 in the numerator and the denominator cancel out and your are left with:
.
either way gets you the same answer.