document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114805>Question 1114805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 100 patients in a hospital with a certain disease. Of these, 10 are selected to undergo a drug treatment that increases the percentage cured rate from 50 percent to 75 percent. What is the probability that the patient received a drug treatment if the patient is known to be cured? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729731 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=729731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is what i think it will be.\r<BR>\n" );
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document.write( "the probability that a patient receives the drug treatment is 10/100 = .1\r<BR>\n" );
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document.write( "the formula for that is p(D) = .1\r<BR>\n" );
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document.write( "10% of the time, the patient is cured using the drug, and 90% of the time the patient is cured without taking the drug.\r<BR>\n" );
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document.write( "the formula for that is p(C) = .1 * .75 + .9 * .5 = .525\r<BR>\n" );
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document.write( "the probability that a person is cured and has taken the drug is .1 * .75 = .075\r<BR>\n" );
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document.write( "the formula for that is p(C and D) = .075\r<BR>\n" );
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document.write( "given that a person is cured, what is the probability that the person took the drug.\r<BR>\n" );
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document.write( "the formula for that is p(D given C) = p(C and D) / p(C).\r<BR>\n" );
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document.write( "that becomes p(D given C) = .075 / .525 = .1428571429.\r<BR>\n" );
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document.write( "i usually try an experiment to see if what i did is reasonable.\r<BR>\n" );
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document.write( "my experiment for this problem is as follows.\r<BR>\n" );
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document.write( "assume 1000 patients.\r<BR>\n" );
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document.write( "10% of them receive the drug and 90% of them don't.\r<BR>\n" );
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document.write( "that makes 100 who received the drug and 900 who didn't.\r<BR>\n" );
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document.write( "75% of the ones who took the drug are cured = 75\r<BR>\n" );
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document.write( "50% of the ones who didn't take the drug are cured = 450.\r<BR>\n" );
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document.write( "total number of cured patients = 525.\r<BR>\n" );
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document.write( "525/1000 = .525, so p(C) looks like an accurate ratio.\r<BR>\n" );
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document.write( "given that a person is cured, what is the probability that the person took the drug.\r<BR>\n" );
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document.write( "525 were cured and, out of them, 75 took the drug.\r<BR>\n" );
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document.write( "75/525 = .1428571429, so p(D given C) looks good as well.\r<BR>\n" );
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document.write( "75 patients out of the 1000 gook the drug and were cured.\r<BR>\n" );
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document.write( "p(D and C) = 75 / 1000 = .075, so that ratio looks good as well.\r<BR>\n" );
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document.write( "the solution looks reasonable, so i would go with that.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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