document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092889>Question 1092889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. Assume 64% of the college graduates who cannot find a job are female and that 39% of the college graduates who can find a job are female. Given a male college graduate, find the probability he cannot find a full time job in his chosen profession?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707747 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> set up a table that looks like this:\r<BR>\n" );
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document.write( "               % can find a job         % can't find a job       % total\r\n" );
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document.write( "male                24.4                      21.6                 46.0\r\n" );
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document.write( "female              15.6                      38.4                 54.0\r\n" );
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document.write( "total               40.0                      60.0                100.0\r\n" );
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document.write( "you start off with 60% of all students who can't find a job which means that 40% can.\r<BR>\n" );
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document.write( "you then are told that 64% of the students who can't find a job are female.<BR>\n" );
document.write( "64% of 60% is equal to .64 * .60 = .385 * 100% = 38.4% of all students are females that can't find a job.<BR>\n" );
document.write( "the balance have to be males, therefore 60% - 38.4% = 21.6% of all students are males that can't find a job.\r<BR>\n" );
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document.write( "you then are told that 39% of the students who can find a job are female.<BR>\n" );
document.write( "39% of 40% is equal to .39 * .4 = .156 * 100% = 15.6% of all students are females that can find a job.<BR>\n" );
document.write( "the balance have to be male, therefore 40% - 15.6% = 24.4% of all students are males that can find a job.\r<BR>\n" );
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document.write( "from the table, you can see that the total percent of males is 46% and the total percent of females is 54%.\r<BR>\n" );
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document.write( "you are asked to find the probability that a graduate cannot find a job given that he is a male.\r<BR>\n" );
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document.write( "the probability that he is a male is 46%.\r<BR>\n" );
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document.write( "the probability that he is a male and can't find a job is 21.6%.\r<BR>\n" );
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document.write( "21.6 / 46 = .4695652174\r<BR>\n" );
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document.write( "the probability that a college student can't find a job given that he is a male is .4695652174 which is equal to 46.96% rounded to 2 decimal places.\r<BR>\n" );
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document.write( "this might make more sense if you put it into numbers.\r<BR>\n" );
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document.write( "assume 1000 students in total\r<BR>\n" );
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document.write( "60% can't find a job.<BR>\n" );
document.write( "40% can.\r<BR>\n" );
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document.write( "this means 600 can't find a job and 400 can.\r<BR>\n" );
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document.write( "64% of the ones who can't find a job are female.<BR>\n" );
document.write( "this means that .64 * 600 = 384 female who can't find a job.<BR>\n" );
document.write( "this means that 600 - 384 = 216 males who can't find a job.\r<BR>\n" );
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document.write( "39% of the one who can find a job are female.<BR>\n" );
document.write( "this means that .39 * 400 = 156 females who can find a job.<BR>\n" );
document.write( "this means that 400 - 156 = 244 males who can find a job.\r<BR>\n" );
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document.write( "add up the total females and you get 384 who can't find a job plus 156 who can for a total of 540 female graduates.\r<BR>\n" );
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document.write( "add up the total males and you get 216 who can't find a job and 244 who can for a total of  460 male graduates.\r<BR>\n" );
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document.write( "your table will look like this:\r<BR>\n" );
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document.write( "               % can find a job         % can't find a job       % total\r\n" );
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document.write( "male                244                       216                  460\r\n" );
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document.write( "female              156                       384                  540\r\n" );
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document.write( "total               400                       600                 1000\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "you want to know the probability that a student can't find a job in his profession given that the student is a male.\r<BR>\n" );
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document.write( "216 male students can't find a job.<BR>\n" );
document.write( "the number of male students is equal to 460.\r<BR>\n" );
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document.write( "the probability that a student can't find a job given that the student is a male is equal to 216 / 460 = .4695652174\r<BR>\n" );
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document.write( "the formula to use is:\r<BR>\n" );
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document.write( "probability that a student can't find a job given that the students is a male is equal to the probability that the student is a male and can't find a job divided by the probability that the student is a male.\r<BR>\n" );
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document.write( "in algebraic terms, this would be p(NJ given M) = p(NJ and M) / p(M)\r<BR>\n" );
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document.write( "p(M) is the probability that the student is a male.<BR>\n" );
document.write( "p(NJ and M) is the probability that the student can't find a job and is a male.\r<BR>\n" );
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document.write( "from the first table, you can see that:\r<BR>\n" );
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document.write( "p(M) = 46%<BR>\n" );
document.write( "p(NJ and M) = 21.6%\r<BR>\n" );
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document.write( "p(NJ given M) = p(NJ and M) / p(M) = 21.6% / 46% = .4695652174\r<BR>\n" );
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document.write( "that equivalent to 46.96% rounded to 2 decimal places.\r<BR>\n" );
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document.write( "from the second table you can see that the number of men out of a total 1000 students who can't find a job is 216 and that there are 460 men.\r<BR>\n" );
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document.write( "216/460 = .4695652174 which is equal to 46.96% rounded to 2 decimal places.\r<BR>\n" );
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document.write( "the number of students was chosen to be 1000 because the arithmetic was easier that way and there was a direct correlation to the percents.\r<BR>\n" );
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document.write( "any number of student could have been used and you would get the same percentages.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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