document.write( "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.
\n" ); document.write( "In the table are these #'s under these headings from Left to Right.
\n" ); document.write( " Employed******/*********Unemployed
\n" ); document.write( "Male 67761*********/*********2433
\n" ); document.write( "Female 58655*********/*********2285
\n" ); document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #328203 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
your table is as follows if i understand it correctly:
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document.write( "             employed         unemployed\r\n" );
document.write( "male           67761               2433\r\n" );
document.write( "female         58655               2285\r\n" );
document.write( "

\n" ); document.write( "the question is:
\n" ); document.write( "find the probability of selecting a person who is employed, given that the person is male.
\n" ); document.write( "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.
\n" ); document.write( "that would be:
\n" ); document.write( " $\"67761+%2F+%2867761+%2B+2433%29+=+.965338918\"$
\n" ); document.write( "the probability of getting an employed male is .965338918.
\n" ); document.write( "this is because .965338918 * the total number of males is employed.
\n" ); document.write( "-----
\n" ); document.write( "there is a formula that says that:
\n" ); document.write( "p(e|m) = $\"p%28e+and+m%29+%2F+p%28m%29\"$
\n" ); document.write( "this formula states:
\n" ); document.write( "the probability of e given m is equal to the probability of (e intersect m) divided by the probability of m.
\n" ); document.write( "e is employed
\n" ); document.write( "m is male.
\n" ); document.write( "this formula will also give you the same answer, but the numbers are derived as follows:
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document.write( "            employed          unemployed         total\r\n" );
document.write( "male          67761              2433            70164\r\n" );
document.write( "female        58655              2285            60940\r\n" );
document.write( "total        126416              4718           131134\r\n" );
document.write( "

\n" ); document.write( "p(e and m) is equal to $\"67761+%2F+131134+=+.516730977\"$
\n" ); document.write( "p(m) is equal to $\"70164+%2F+131134+=+.535055745\"$
\n" ); document.write( "p(e|m) = $\"p%28e+and+m%29+%2F+p%28m%29+=+.516730977+%2F+.535055745+=+.965338918\"$
\n" ); document.write( "it's exactly the same as we derived above.
\n" ); document.write( "in the first way we figured it out, our universe became only the men.
\n" ); document.write( "in the second way we figured it out, our universe was everybody.
\n" ); document.write( "the formulas give you the same number.
\n" ); document.write( "the first method was $\"67761+%2F+70164\"$ which was the number of employed males divided by the total number of males.
\n" ); document.write( "the second method was:
\n" ); document.write( " $\"p%28e+and+m%29+%2F+p%28m%29\"$
\n" ); document.write( " $\"p%28e+and+m%29+=+67761+%2F+131134\"$
\n" ); document.write( " $\"p%28m%29+=+70164+%2F+131134\"$
\n" ); document.write( " $\"p%28e+and+m%29+%2F+p%28m%29\"$ becomes $\"%2867761%2F131134%29+%2F+%2870164%2F131134%29\"$ which is equivalent to:
\n" ); document.write( " $\"%2867761%2F131134%29+%2A+%28131134%2F70164%29\"$ which is equivalent to:
\n" ); document.write( " $\"%2867761+%2A+131134%29+%2F+%28131134+%2A+70164%29\"$
\n" ); document.write( "the 131134 in the numerator and the denominator cancel out and your are left with:
\n" ); document.write( " $\"%2867761%2F70164%29\"$ .
\n" ); document.write( "either way gets you the same answer.\r
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