document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018521>Question 1018521</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A local university found it could classify its students into one of three general categories: morning students (43%), afternoon students (28%), and evening students.  38% of the morning students, 25% of the afternoon students, and 23% of the evening students live on campus. <BR>\n" );
document.write( "What is the probability a non-afternoon student does not live on campus? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634614 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=634614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the easiest way to see this is to create a table.\r<BR>\n" );
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document.write( "the first table will include all students.\r<BR>\n" );
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document.write( "the second table will include only non-afternoon students (only morning and evening).\r<BR>\n" );
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document.write( "the first table that includes all students is shown below:\r<BR>\n" );
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document.write( "              on campus        not on campus       total\r\n" );
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document.write( "morning          16.34             26.66             43\r\n" );
document.write( "afternoon        7                 21                28\r\n" );
document.write( "evening          6.67              22.33             29\r\n" );
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document.write( "total            30.01             69.99             100\r\n" );
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document.write( "the second table includes all students who are not afternoon students.\r<BR>\n" );
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document.write( "              on campus        not on campus       total\r\n" );
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document.write( "morning          16.34             26.66             43\r\n" );
document.write( "evening          6.67              22.33             29\r\n" );
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document.write( "total            23.01             48.99             72\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "these are percent tables.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "the percent of students who are morning students is 43%.<BR>\n" );
document.write( "38% of these live on campus, so .38 * 43 = 16.34% of all students live on campus and are morning students.<BR>\n" );
document.write( "62% of these do not live on campus, so .62 * 43 = 26.66% of all students do not live on campus and are morning students.\r<BR>\n" );
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document.write( "the second table includes only the students who are not afternoon students.\r<BR>\n" );
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document.write( "in the second table, the total of all students who are not afternoon students is equal to 72%.\r<BR>\n" );
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document.write( "in the second table, the total of all students who do not live on campus is 48.99%\r<BR>\n" );
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document.write( "this tells you that the percent of student who are not afternoon students and who do not live on campus is 48.99 / 72 = .68041666... = 68.041666...%.\r<BR>\n" );
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document.write( "this says that approximately 68.04% of the students who are not afternoon students do not live on campus.\r<BR>\n" );
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document.write( "your answer, as best i can determine, is that approximately 68.04% of the students who are not afternoon students do not live on campus.\r<BR>\n" );
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document.write( "an assumed real world example should help cement the understanding.\r<BR>\n" );
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document.write( "assume the total number of students is 25,000<BR>\n" );
document.write( "43% of 25,000 = 10750<BR>\n" );
document.write( "28% of 25,000 = 6250<BR>\n" );
document.write( "29% of 25,000 = 7250\r<BR>\n" );
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document.write( "total of 10750 + 7250 are not afternoon students = 18000.\r<BR>\n" );
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document.write( "18000/25000 = .72 = 72% of all the students are not afternoon students.\r<BR>\n" );
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document.write( "62% of the 10750 do not live on campus = 6665.<BR>\n" );
document.write( "77% of the 7250 do not live on campus = 5582.5\r<BR>\n" );
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document.write( "total of the 18000 who do not live on campus is 12247.5\r<BR>\n" );
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document.write( "this is equal to 12247.5 / 18000 = roughly 68.04%\r<BR>\n" );
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document.write( "numbers check out so the solution appears to be good whether you work with percents or assumed actual numbers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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