document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192485>Question 1192485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1 point) Suppose that P(A)=0.4, P(C∣A)=0.0055, and P(C′∣A′)=0.0105. Find P(A∣C) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824359 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=824359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "P(A) = 0.4<BR>\n" );
document.write( "P(A') = 1 - P(A) = 1 - 0.4 = 0.6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(C | A) = 0.0055<BR>\n" );
document.write( "P(C' | A) = 1 - P(C | A) = 1 - 0.0055 = 0.9945\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(C' | A') = 0.0105<BR>\n" );
document.write( "P(C | A') = 1-P(C' | A') = 1-0.0105 = 0.9895\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To summarize so far, we have:<BR>\n" );
document.write( "P(A) = 0.4<BR>\n" );
document.write( "P(A') = 0.6<BR>\n" );
document.write( "P(C|A) = 0.0055<BR>\n" );
document.write( "P(C|A') = 0.9895\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the Law of Total Probability to be able to say the following<BR>\n" );
document.write( "P(C) = P(C and A) + P(C and A')<BR>\n" );
document.write( "P(C) = P(C | A)*P(A) + P(C | A')*P(A')<BR>\n" );
document.write( "P(C) = 0.0055*0.4 + 0.9895*0.6<BR>\n" );
document.write( "P(C) = 0.5959\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, apply Bayes Theorem<BR>\n" );
document.write( "P(A | C) = P(C | A)*P(A)/P(C)<BR>\n" );
document.write( "P(A | C) = 0.0055*0.4/0.5959<BR>\n" );
document.write( "P(A | C) = <font color=red>0.0036918946132</font><BR>\n" );
document.write( "The result is approximate.<BR>\n" );
document.write( "Round that value however you need to.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's one useful calculator to check your work.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.gigacalculator.com/calculators/bayes-theorem-calculator.php\">https://www.gigacalculator.com/calculators/bayes-theorem-calculator.php</a><BR>\n" );
document.write( "Type in these values<BR>\n" );
document.write( "P(A) = 0.4<BR>\n" );
document.write( "P(C|A) = 0.0055<BR>\n" );
document.write( "P(C|A') = 0.9895<BR>\n" );
document.write( "Make sure to click the radio button labeled \"Proportions e.g. 0.05\" before hitting \"calculate\".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src=\"https://i.imgur.com/A7JFjYZ.png\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );