document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909941>Question 909941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in an exam only 20% failed in maths and 15% failed in chemistry and 10% failed in both maths and chemistry. determine probability student selected in random has passed maths and chemistry </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #552154 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=552154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20% failed math<BR>\n" );
document.write( "15% failed chemistry<BR>\n" );
document.write( "10% failed both.\r<BR>\n" );
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document.write( "p(a or b) = p(a) + p(b0 - p(ab)\r<BR>\n" );
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document.write( "in this problem, this becomes:\r<BR>\n" );
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document.write( "p(fail math or chem) = p(fail math) + p(fail chem) - p(fail both math and chem).\r<BR>\n" );
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document.write( "that becomes:\r<BR>\n" );
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document.write( "p(fail math or chem) = .20 + .15 - .10 = .25\r<BR>\n" );
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document.write( "this mean that 25% failed math or chem or both.\r<BR>\n" );
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document.write( "that means that 75% didn't fail either one which means that they passed both.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "i also looked at it another way.\r<BR>\n" );
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document.write( "if 10% failed both, that means that 90% passed one or the other or both.\r<BR>\n" );
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document.write( "p(a or b) = p(a) + p(b) - p(ab).\r<BR>\n" );
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document.write( "that becomes:\r<BR>\n" );
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document.write( "p(pass math or chem or both) = p(pass math) + p(pass chem) - p(pass math and chem).\r<BR>\n" );
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document.write( "we know that p(pass math or chem or both) = 90%.\r<BR>\n" );
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document.write( "we know that p(pass math) = 80%\r<BR>\n" );
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document.write( "we know that p(pass chem) = 85%)\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "p(pass math or chem or both) = p(pass math) + p(pass chem) - p(pass math and chem) becomes:\r<BR>\n" );
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document.write( "90% = 80% + 85% - p(pass math and chem).\r<BR>\n" );
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document.write( "solve for p(pass math and chem) and you get:\r<BR>\n" );
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document.write( "p(pass math and chem) = 80% + 85% - 90% = 165% - 90% = 75%.\r<BR>\n" );
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document.write( "looks good either way so I'll go with that.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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