document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026011>Question 1026011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One cage contains 3 white mice and 2 black ones, and another cage contains 5 white mice and 2 black ones.  A cage is chosen at random and three mice are selected.  Find the expected number of white mice in the sample. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641271 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=641271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that each cage is equally likely to be chosen.<BR>\n" );
document.write( "Let X = the number of white mice in the three mice chosen<BR>\n" );
document.write( "Apparently, x = 0, 1, 2, 3.<BR>\n" );
document.write( "Given the first cage is chosen, the following are the conditional probabilities for each value of X.<BR>\n" );
document.write( "X -----> 0      1       2     3<BR>\n" );
document.write( "p(x|1st cage)---> 0    3/10     6/10   1/10\r<BR>\n" );
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document.write( "Given the second cage is chosen, the following are the conditional probabilities for each value of X.<BR>\n" );
document.write( "X -----> 0      1       2     3<BR>\n" );
document.write( "p(x|2nd cage)---> 0    1/7      4/7   2/7\r<BR>\n" );
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document.write( "This means the combined (joint) probability mass function is as follows:\r<BR>\n" );
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document.write( "X -----> 0      1          2          3<BR>\n" );
document.write( "p(x)---> 0    62/280     164/280     54/280\r<BR>\n" );
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document.write( "==> E(X) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2A0+%2B+1%2A%2862%2F280%29+%2B+2%2A%28164%2F280%29+%2B+3%2A%2854%2F280%29+=+1.97143 ALIGN=MIDDLE  ALT=\"0%2A0+%2B+1%2A%2862%2F280%29+%2B+2%2A%28164%2F280%29+%2B+3%2A%2854%2F280%29+=+1.97143\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus, the expected number of white mice in the selection is practically 2.  </SPAN>\n" );
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