document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180305>Question 1180305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A few people who have a particular disease take part in a medical trial that tests the effect of a medicine on the disease. Half the people are given medicine and the other half are given sugar pills, which have no effect on the disease. The medicine has a 60% chance of curing someone, but people who do not get the medicine still have a 10% chance of getting well.\r<BR>\n" );
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document.write( "The probability that a person gets well is ? %, and the probability that the person was cured because of the medicine is <BR>\n" );
document.write( "? %<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810061 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 0.5 are given the medicine, which has a 0.60 probability of cure, so that is 0.30 of the total who will be cured.<BR>\n" );
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document.write( "0.5*0.10=0.05.<BR>\n" );
document.write( "The probability the person got well over all is 35%<BR>\n" );
document.write( "       C===  NC===Tot<BR>\n" );
document.write( "M=  60 ==40 ==100<BR>\n" );
document.write( "P =   10==  90= 100<BR>\n" );
document.write( "Tot-70--130--200\r<BR>\n" );
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document.write( "The last part is not clear. There is a 60% probability someone was cured because of the medicine.  That is known.<BR>\n" );
document.write( "BUT, given that someone was cured, the probability that they had taken the medicine was 6/7 or 86%.  That is a different statement.\r<BR>\n" );
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document.write( "This is an extremely important distinction to make in medicine and other places.  Just because B followed A doesn't mean that A caused B.   </SPAN>\n" );
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