document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1024793>Question 1024793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose E,F are events in a sample space S. Suppose Pr (E|F)=3/4 and Pr (F|E)= 1/2 and Pr (EUF)=2/3. Find Pr (E) and Pr (F) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640225 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(E|F) = P(E&#8745;F)/P(F) ==>P(F) = (4/3)P(E &#8745; F)<BR>\n" );
document.write( "P(F|E) = P(E&#8745;F)/P(E) ==>P(E) = 2P(E &#8745; F)\r<BR>\n" );
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document.write( "==> P(E U F) = P(E) + P(F) - P(E &#8745;F) = 2P(E &#8745; F) +  (4/3)P(E &#8745; F) - P(E &#8745;F) = (7/3)P(E &#8745;F)\r<BR>\n" );
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document.write( "==> 2/3 = (7/3)P(E &#8745;F)\r<BR>\n" );
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document.write( "==> 2 = 7P(E &#8745;F), or\r<BR>\n" );
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document.write( "P(E &#8745;F) = 2/7.\r<BR>\n" );
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document.write( "==> P(E) = 2P(E &#8745; F) = 4/7, and \r<BR>\n" );
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document.write( "==> P(F) = (4/3)P(E &#8745; F) = 8/21. </SPAN>\n" );
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