document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068989>Question 1068989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am enrolled in an online Math 125 class. I posted this question earlier in the week and never got a response, so here I am! I am just not understanding these questions. I made the tree diagram as suggested and put all the information at the bottom how I worked the problem out. It is just super confusing, and I can't seem to find anything that helps me work this problem out. Any help would be appreciated! Thanks!\r<BR>\n" );
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document.write( "A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event \"the person is infected\" and B be the event \"the person tests positive\".\r<BR>\n" );
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document.write( "a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign.\r<BR>\n" );
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document.write( "b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.\r<BR>\n" );
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document.write( "                                             .80 Positive Test Result  +\r<BR>\n" );
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document.write( "                 .005 Infected\r<BR>\n" );
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document.write( "                                             .20 Negative Test Result --\r<BR>\n" );
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document.write( "Tested                                    \r<BR>\n" );
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document.write( "                                             .10 Positive Test Result  +    \r<BR>\n" );
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document.write( "                 .995 Not Infected\r<BR>\n" );
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document.write( "                                              .90 Negative Test Result --\r<BR>\n" );
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document.write( "I believe the answer that I got for part (a) was 3.8%. I didn't try part (b) since I couldn't find the correct answer for part (a).\r<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 #684258 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=684258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event \"the person is infected\" and B be the event \"the person tests positive\".<BR>\n" );
document.write( "P(infected) = 1/200<BR>\n" );
document.write( "P(not infected) = 199/200<BR>\n" );
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document.write( "P(A) = 1/200 ; P(A') = 199/200<BR>\n" );
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document.write( "P(B|A') = 0.1<BR>\n" );
document.write( "P(B|A) = 0.8 ; P(B'|A) = 0.2<BR>\n" );
document.write( "P(B|A) = P(test positive | infected) = 0.80 <BR>\n" );
document.write( "P(A'|B) = P(is not infected | test positive) = 0.10 <BR>\n" );
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document.write( "a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the' nearest tenth of a percent and do not include a percent sign.<BR>\n" );
document.write( "P(A|B) = P(B and A)/P(B) = P(B|A)*P(A)/P(B)<BR>\n" );
document.write( "= P(B|A)P(A)/[P(B and A)+P(B and A')<BR>\n" );
document.write( "= P(B|A)P(A)/[P(B|A)P(A)+P(B|A')P(A')]<BR>\n" );
document.write( "= [0.8*(1/200)]/[0.8*(1/200) + 0.1*(199/200)]<BR>\n" );
document.write( "= 0.004/[0.004+ 0.104]<BR>\n" );
document.write( "= 0.037<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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