document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167002>Question 1167002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following scenario:<BR>\n" );
document.write( "• Let P(C) = 0.5<BR>\n" );
document.write( "• Let P(D) = 0.6<BR>\n" );
document.write( "• Let P(C | D) = 0.7\r<BR>\n" );
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document.write( "Are C and D mutually exclusive? Why or why not?\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 #791575 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52914)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Tutor  &nbsp;@solver91311 just gave you the correct answer.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I also want to add my &nbsp;2 &nbsp;cents.\r<BR>\n" );
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document.write( "The condition  P(C|D) = 0.7  just tells you that the events C and D are not mutually exclusive.\r\n" );
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document.write( "     Otherwise,  P(C|D)  would be zero, by the definition of mutually exclusive events.\r\n" );
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document.write( "But, actually, this condition P(C|D) = 0.7 is EXCESSIVE.\r\n" );
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document.write( "Two conditions, P(C) = 0.5 and P(D) = 0.6  are just ENOUGH to conclude that the the events C and D are not mutually exclusive.\r\n" );
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document.write( "Indeed, otherwise it would be \r\n" );
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document.write( "    P(C U D) = P(C) + P(D) = 0.5 + 0.6 = 1.1 > 1   (for mutually exclusive events, probabilities are added (!) )\r\n" );
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document.write( "which is IMPOSSIBLE.\r\n" );
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document.write( "So, &nbsp;again, &nbsp;having two conditions &nbsp;P(C) = 0.5 &nbsp;and &nbsp;P(D) = 0.6 &nbsp;is just enough to conclude \r<BR>\n" );
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document.write( "that the events &nbsp;C &nbsp;and D &nbsp;&nbsp;ARE &nbsp;NOT &nbsp;mutually exclusive.\r<BR>\n" );
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