document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061858>Question 1061858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "I am asking for a tutor to look and see if my answer is correct\r<BR>\n" );
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document.write( "A certain virus infects one in every 500 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. 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( "\"What is the probability that a person does not have the virus given that they have tested negative.\" Of the 180 people who are infected, .1(180)= 18 will text negative. Of the 99800 people who are not infected, .9(99800)= 89820 will test negative. Of the 89820+ 18= 89838 people who tested negative 89820 do not have the virus so the probability a person who tested negative does not have the virus is 89820/89832= 0.999 or about 99.9%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676635 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I suspect that the answer may end up being almost the same, but<BR>\n" );
document.write( "why do you start assuming that you have a population where<BR>\n" );
document.write( "180 people are infected and 99800 are uninfected?<BR>\n" );
document.write( "That would be a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2B99800=99980 ALIGN=MIDDLE  ALT=\"180%2B99800=99980\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the ratio of infected to total would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F99980=18%2F9998=approximately ALIGN=MIDDLE  ALT=\"180%2F99980=18%2F9998=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F9999=2%2F1111=1%2F555.5 ALIGN=MIDDLE  ALT=\"18%2F9999=2%2F1111=1%2F555.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means 1 person out of 555.5 people would be infected,<BR>\n" );
document.write( "and that counts as a mistake.<BR>\n" );
document.write( " <BR>\n" );
document.write( "You could have started with 100,000 people.<BR>\n" );
document.write( "Of those, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100000%2F500=200 ALIGN=MIDDLE  ALT=\"100000%2F500=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > are infected,<BR>\n" );
document.write( "and the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100000-200=99800 ALIGN=MIDDLE  ALT=\"100000-200=99800\"   DISABLED_style= \"max-width:90%; height:auto;\" > are uninfected.<BR>\n" );
document.write( "Of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200 ALIGN=MIDDLE  ALT=\"200\"   DISABLED_style= \"max-width:90%; height:auto;\" > infected people,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%28200%29=20 ALIGN=MIDDLE  ALT=\"0.1%28200%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > will test negative.<BR>\n" );
document.write( "Of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99800 ALIGN=MIDDLE  ALT=\"99800\"   DISABLED_style= \"max-width:90%; height:auto;\" > uninfected,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9%2899800%29=89820 ALIGN=MIDDLE  ALT=\"0.9%2899800%29=89820\"   DISABLED_style= \"max-width:90%; height:auto;\" > will test negative, as you said.<BR>\n" );
document.write( "The total number of people testing negative is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2B89820=89840 ALIGN=MIDDLE  ALT=\"20%2B89820=89840\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Comparing to that number, the number of uninfected people is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=89820%2F89840=0.999777 ALIGN=MIDDLE  ALT=\"89820%2F89840=0.999777\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded), which could be stated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2299.98%25%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%2299.98%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "NOTES:<BR>\n" );
document.write( "With your calculation you should get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=89820%2F89838=0.999800 ALIGN=MIDDLE  ALT=\"89820%2F89838=0.999800\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded), which could be stated as 99.98%.<BR>\n" );
document.write( "You mistakenly wrote your final calculation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=89820%2F89832=0.999866 ALIGN=MIDDLE  ALT=\"89820%2F89832=0.999866\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded), which could be stated as 99.99%.<BR>\n" );
document.write( "Neither of those numbers can be rounded to 99.9%;<BR>\n" );
document.write( "they would round to 100.0% if we only give them one decimal digit.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Note that before the test,<BR>\n" );
document.write( "a person knew that the probability of being uninfected was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=499%2F500=0.998000 ALIGN=MIDDLE  ALT=\"499%2F500=0.998000\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 99.80%.<BR>\n" );
document.write( "If this virus is life-threatening (or life-altering),<BR>\n" );
document.write( "people may want to know more.<BR>\n" );
document.write( "If they test positive, maybe there is something they can do about it.<BR>\n" );
document.write( "If they test negative,<BR>\n" );
document.write( "going from 99.80% to 99.98% sure that they are safe may be cause for celebration. </SPAN>\n" );
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