document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085606>Question 1085606</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Use the multiplication rule for dependent events to solve for the following: A presenter needs two volunteers to help with an experiment. There are 30 total people to select from; 18 are women and 12 are men. He randomly chooses one volunteer who comes to the front of the room. He then chooses a second volunteer from those still seated. What is the probability that both volunteers chosen are women? Start with: \r<BR>\n" );
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document.write( "P(woman 1st and woman 2nd) =<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 #699847 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( " Use the multiplication rule for dependent events to solve for the following: A presenter needs two volunteers to help with an experiment. There are 30 total people to select from; 18 are women and 12 are men. He randomly chooses one volunteer who comes to the front of the room. He then chooses a second volunteer from those still seated. What is the probability that both volunteers chosen are women? Start with: \r<BR>\n" );
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document.write( "P(woman 1st and woman 2nd) =<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Step 1:<BR>\n" );
document.write( "From 18 women and 12 men,<BR>\n" );
document.write( "P(woman)=18/30<BR>\n" );
document.write( "Step 2:<BR>\n" );
document.write( "From 17 women and 12 men,<BR>\n" );
document.write( "P(woman)=17/29<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Apply multiplication rule, <BR>\n" );
document.write( "P(woman,woman)=18/30*17/29=51/145<BR>\n" );
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document.write( "Alternatively, apply hypergeometric distribution:<BR>\n" );
document.write( "W=18<BR>\n" );
document.write( "M=12<BR>\n" );
document.write( "w=number of women chosen<BR>\n" );
document.write( "m=number of men chosen<BR>\n" );
document.write( "P(w,m)=C(W,w)*C(M,m)/C(W+M,w+m)<BR>\n" );
document.write( "where<BR>\n" );
document.write( "C(n,r)=combination of r chosen from n)=n!/(r!(n-r)!)<BR>\n" );
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document.write( "=><BR>\n" );
document.write( "P(2,0)=C(18,2)C(12,0)/C(30,2)<BR>\n" );
document.write( "=51/145 as before. </SPAN>\n" );
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