document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231683>Question 231683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For mutually exclusive events X1, X2, and X3, let P(X1) = .22, P(X2) = .35  and P(X3) = .43. Also, P(Y | Y1) = .40 P(Y|X2) = .30 and P(Y|X3) = .60. Find P(X3|Y)\r<BR>\n" );
document.write( "\n" );
document.write( "A) . 20 B)  . 57 C)  . 38 D)  . 23 \r<BR>\n" );
document.write( "\n" );
document.write( "This theorem is so complicated for me that I dont know where to begin. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171421 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=171421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For mutually exclusive events X1, X2, and X3, <BR>\n" );
document.write( "let P(X1) = .22, P(X2) = .35 and P(X3) = .43. <BR>\n" );
document.write( "Also, P(Y | X1) = .40 P(Y|X2) = .30 and P(Y|X3) = .60. <BR>\n" );
document.write( "Find P(X3|Y)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(X3 | Y) = P(X3 and Y)/P(Y)<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "You are told P(Y | X3) = 0.6<BR>\n" );
document.write( "So P(Y and X3)/P(X3) = 0.6<BR>\n" );
document.write( "and P(Y and X3)/0.43 = 0.6<BR>\n" );
document.write( "So, P(Y and X3) = 0.43*0.6 = 0.258<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "Using that result you have:<BR>\n" );
document.write( "P(X3 | Y) = 0.258/P(Y)<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "But P(Y) = P(Y|X1) + P(Y|X2) + P(Y|X3) = 0.4 + 0.3 + 0.6 = 1.3<BR>\n" );
document.write( "=============================================================<BR>\n" );
document.write( "Final Answer: P(X3 |Y) = 0.258/1.3 = 0.198 <BR>\n" );
document.write( "Round you be 0.20<BR>\n" );
document.write( "which is answer \"A\"<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( "A) . 20 B) . 57 C) . 38 D) . 23 \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );