document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183159>Question 183159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 23 cubes, of which 13 are red.   Three cubes are drawn simultaneously, without replacement.   Let x be the number of red cubes drawn.  Find the expected value of x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137535 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=137535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bag contains 23 cubes, of which 13 are red. Three cubes are drawn simultaneously, without replacement. Let x be the number of red cubes drawn. Find the expected value of x.<BR>\n" );
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document.write( "Random Variable Values: 0,1,2,3<BR>\n" );
document.write( "This is the number of red balls drawn<BR>\n" );
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document.write( "Corresponding Probabilities:<BR>\n" );
document.write( "P(x=0) = 10C3/23C3<BR>\n" );
document.write( "P(x=1) = [13C1*10C2]/23C3<BR>\n" );
document.write( "P(x=2) = [13C2*10C1]/23C3<BR>\n" );
document.write( "P(x=3) = 13C3/23C3<BR>\n" );
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document.write( "To calculate the \"expected value\",<BR>\n" );
document.write( "Multiply each random variable value by its probability.<BR>\n" );
document.write( "Then add up the 4 products.<BR>\n" );
document.write( "That is the expected value of \"x\".<BR>\n" );
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document.write( "[10C3/23C3]*0 = 0<BR>\n" );
document.write( "[[13C1*10C2]/23C3]*1 = 0.3303<BR>\n" );
document.write( "[[13C2*10C1]/23C3]*2 = 0.8807<BR>\n" );
document.write( "[13C3/23C3]*3 = 0.4845<BR>\n" );
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document.write( "Adding you get 0.3303+-8807+.4845 = 1.7<BR>\n" );
document.write( "That is the expected value of \"x\".\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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