document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041391>Question 1041391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the general population, one woman in ten will develop breast cancer. Research has shown that 1 women in 550 carries a mutation of the BRCA gene. Nine out of 10 women with this mutation develop breast cancer. \r<BR>\n" );
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document.write( "A) Find the probability that a randomly selected women will develop breast cancer given that she has a mutation of the BRCA gene. Round to one decimal place as needed.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656366 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=656366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I read the question as it is written, we know that probability. Given that a woman has a mutation, she has a 90% chance of developing breast cancer.  What we do't know is give that a woman has a breast cancer, what is the probability that she has a mutation?<BR>\n" );
document.write( "Let P(Mutation)=B<BR>\n" );
document.write( "P(Cancer)=A<BR>\n" );
document.write( "p(B|A)=p(B)(P(A/B)/p(A)=(1/550)(9/10)/(1/10), and that is 9/550=0.02<BR>\n" );
document.write( "Set up as a table\r<BR>\n" );
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document.write( "=============BRCA+======BRCA-====Total<BR>\n" );
document.write( "CA+------------90--------5410--------- 5500<BR>\n" );
document.write( "CA-------------10--------49490-------49500<BR>\n" );
document.write( "Total--------100---------54900-------55000 (start with a total that will give integers and of that total 1/550 have BRCA+, or 100, and that goes as shown.)Then the CA+ and CA- can be filled in for BRCA, and the final two spaces can be filled.<BR>\n" );
document.write( "To find P(BRCA+/CA+), given there is a cancer, what is the probability the woman is BRCA+, we find it is 90/5500=0.0164 or 0.02.<BR>\n" );
document.write( "Tables are a good way to do these if one can't remember Bayes' Theorem.  Note again that I changed the question.  As it is written, the answer is known. </SPAN>\n" );
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