document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088141>Question 1088141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider an urn containing black and white balls of which 30% are <BR>\n" );
document.write( "black. A simple random sample of five balls is taken. Suppose that <BR>\n" );
document.write( "the urn contains 10 balls.\r<BR>\n" );
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document.write( "a. How many possible samples are there?\r<BR>\n" );
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document.write( "b. How many of these samples will contain no black balls? <BR>\n" );
document.write( "How many will contain exactly one black ball? <BR>\n" );
document.write( "How many will contain 2? <BR>\n" );
document.write( "Three? <BR>\n" );
document.write( "Four? <BR>\n" );
document.write( "Five?<BR>\n" );
document.write( "c. Can you relate the results to probabilities? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702968 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider an urn containing black and white balls of which 30% are <BR>\n" );
document.write( "black.  A simple random sample of five balls is taken. Suppose that <BR>\n" );
document.write( "the urn contains 10 balls.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "30% of 10 is 3.  So there are 3 black balls and 7 white balls.\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "a. How many possible samples are there? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "10 balls Choose 5 = 10C5 = 252 samples\r\n" );
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document.write( "b. How many of these samples will contain no black balls? <BR>\n" );
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document.write( "7 white balls Choose 5 = 7C5 = 21\r\n" );
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document.write( "How many will contain exactly one black ball? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That's 1 black ball and 4 white balls.\r\n" );
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document.write( "(3 back balls Choose 1)(7 white balls Choose 4) = (3C1)(7C4) = \r\n" );
document.write( "(3)(35) = 105\r\n" );
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document.write( "How many will contain 2? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That's 2 black ball and 3 white balls.\r\n" );
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document.write( "(3 back balls Choose 2)(7 white balls Choose 3) = (3C2)(7C3) = \r\n" );
document.write( "(3)(35) = 105\r\n" );
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document.write( "Three? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That's 3 black balls and 2 white balls.\r\n" );
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document.write( "(3 back balls Choose 3)(7 white balls Choose 2) = (3C3)(7C2) = \r\n" );
document.write( "(1)(21) = 21\r\n" );
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document.write( "Four?<BR>\n" );
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document.write( "None, for there are only 3 black balls\r\n" );
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document.write( "Five? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Also none, for there are only 3 black balls\r\n" );
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document.write( "c. Can you relate the results to probabilities?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "P(no black balls) = 21/252 = 1/12\r\n" );
document.write( "P(1 black ball) = 105/252 = 5/12\r\n" );
document.write( "P(2 black balls) = 105/252 = 5/12\r\n" );
document.write( "P(3 black balls) = 21/252 = 1/12\r\n" );
document.write( "P(4 black balls) = 0/252 = 0\r\n" );
document.write( "P(5 black balls) = 0/252 = 0\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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