document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206319>Question 1206319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample is selected from one of two populations, <BR>\n" );
document.write( "S1 and S2,<BR>\n" );
document.write( " with <BR>\n" );
document.write( "P(S1) = 0.7<BR>\n" );
document.write( " and <BR>\n" );
document.write( "P(S2) = 0.3.<BR>\n" );
document.write( " The probabilities that an event A occurs, given that event <BR>\n" );
document.write( "S1<BR>\n" );
document.write( " or <BR>\n" );
document.write( "S2<BR>\n" );
document.write( " has occurred are<BR>\n" );
document.write( "P(A|S1) = 0.2<BR>\n" );
document.write( " and <BR>\n" );
document.write( "P(A|S2) = 0.1.<BR>\n" );
document.write( "Use the Law of Total Probability to find P(A). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843683 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52782)</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=843683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "As with other today's posts (and, generally, with many other posts at this forum),<BR>\n" );
document.write( "the problem formulation is INCORRECT.\r<BR>\n" );
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document.write( "It is incorrect, because it is incomplete.\r<BR>\n" );
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document.write( "To be complete, it must say in the condition, that populations S1 and S2 are disjoint (= mutually exclusive).\r<BR>\n" );
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document.write( "The fact that &nbsp;P(S1) + P(S2) = 0.7 + 0.3 = 1 &nbsp;does not imply automatically that &nbsp;S1 &nbsp;and &nbsp;S2 &nbsp;are disjoint, <BR>\n" );
document.write( "since they still may have intersection &nbsp;(for example, &nbsp;S2 &nbsp;can be a part of &nbsp;S1).\r<BR>\n" );
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document.write( "Edwin, I do not read in the head of the instructor.\r<BR>\n" );
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document.write( "I even do not try to do it . . . \r<BR>\n" );
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document.write( "I read what I see in the post.\r<BR>\n" );
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