document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426048>Question 426048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Would you please be able to help me with this question? I am lost!\r<BR>\n" );
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document.write( "in a certain small town, 16% of the population developed lung cancer. if 45% of the population are smokers, and 85% of those developing lung cancer are smokers, what is the probability that a smoker in this population will develop lung cancer? \r<BR>\n" );
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document.write( "thank you very much for your time and help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296493 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=296493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given:\r<BR>\n" );
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document.write( ".85 of those developing lung cancer are smokers.<BR>\n" );
document.write( ".16 of the population developed lung cancer.\r<BR>\n" );
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document.write( "this means that .85 * .16 = .136 of the population developed lung cancer and also smoked.\r<BR>\n" );
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document.write( "the smokers, however, only make up .45 of the population.\r<BR>\n" );
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document.write( "this means that .136 / .45 = .302222222 of the smokers developed lung cancer.\r<BR>\n" );
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document.write( "the probability that a smoker in this population will develop lung cancer is equal to .302222222\r<BR>\n" );
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document.write( "this is a p(a given b) type problem.\r<BR>\n" );
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document.write( "p(a given b) = p(a intersect b) / p(b)\r<BR>\n" );
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document.write( "p(b) is the probability that a person is a smoker.\r<BR>\n" );
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document.write( "p(b) equals .45\r<BR>\n" );
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document.write( "p(a intersect b) is the probability that a person has lung cancer is also a smoker.\r<BR>\n" );
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document.write( "since the probability that the person has lung cancer is .16 and the probability that the person who has lung cancer also smokes is .85, then:\r<BR>\n" );
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document.write( "p(a intersect b) = .16 * .85 = .136\r<BR>\n" );
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document.write( "p(a given b) = p(a intersect b) / p(b) = .136 / .45 = .3022222222\r<BR>\n" );
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document.write( "if you are a smoker in this population, then the probability that you will have lung cancer is .302222\r<BR>\n" );
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document.write( "this is based on the previous experience that indicates that .30222222 of the persons in the population who smoked also developed lung cancer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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