document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117797>Question 1117797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question:<BR>\n" );
document.write( "The door prizes at a dance are gift certificates from local merchants. There are four $10 certificates, five $20 certificates, and three $50 certificates. The prize envelopes are mixed together in a bag and are drawn at random.\r<BR>\n" );
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document.write( "Determine the probability distribution for the number of $20 certificates in the first two prizes drawn. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732934 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have:\r<BR>\n" );
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document.write( "4 ten dollar certificates<BR>\n" );
document.write( "5 twenty dollar certificates<BR>\n" );
document.write( "3 fifty dollar certificates.\r<BR>\n" );
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document.write( "that's a total of 12 certificates, 5 of which are twenty dollar certificates and 7 of which are not twenty dollar certificates.\r<BR>\n" );
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document.write( "you are drawing 2 times.\r<BR>\n" );
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document.write( "you can draw:\r<BR>\n" );
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document.write( "0 twenty dollar certificates on the first 2 draws.<BR>\n" );
document.write( "1 twenty dollar certificate on the first draw and 0 twenty dollar certificates on the second draw.<BR>\n" );
document.write( "0 twenty dollar certificates on the first draw and 1 twenty dollar certificate on the second draw.<BR>\n" );
document.write( "2 twenty dollar certificates on the first 2 draws.\r<BR>\n" );
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document.write( "no other options are possible.\r<BR>\n" );
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document.write( "your probabilities will be as follows:\r<BR>\n" );
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document.write( "0 twenty dollar certificates on the first 2 draws.\r<BR>\n" );
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document.write( "the probability will be 7/12 * 6/11 = 42/132.\r<BR>\n" );
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document.write( "1 twenty dollar certificate on the first draw and 0 twenty dollar certificates on the second draw.\r<BR>\n" );
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document.write( "the probability will be 5/12 * 7/11 = 35/132.\r<BR>\n" );
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document.write( "0 twenty dollar certificates on the first draw and 1 twenty dollar certificate on the second draw.\r<BR>\n" );
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document.write( "the probability will be 7/12 * 5/11 = 35/132.\r<BR>\n" );
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document.write( "2 twenty dollar certificates on the first 2 draws.\r<BR>\n" );
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document.write( "the probability will be 5/12 * 4/11 = 20/132.\r<BR>\n" );
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document.write( "your total probabilities will be (42 + 35 + 35 + 20) / 132 = 132/132 = 1.\r<BR>\n" );
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document.write( "since the sum of all probabilities in the probability distribution must be equal to 1, then this is as it should be.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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