document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019597>Question 1019597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected.\r<BR>\n" );
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document.write( "a.  Use technology to find the number of ways 15 employees can be chosen from 200.\r<BR>\n" );
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document.write( "b. Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities.\r<BR>\n" );
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document.write( "c. What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)?\r<BR>\n" );
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document.write( "d. Does your answer to part (c) indicate that the committee selection is biased? Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635558 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=635558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected.<BR>\n" );
document.write( "a.  Use technology to find the number of ways 15 employees can be chosen from 200.<BR>\n" );
document.write( "b. Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities.<BR>\n" );
document.write( "c. What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)?<BR>\n" );
document.write( "d. Does your answer to part (c) indicate that the committee selection is biased? Explain your reasoning.<BR>\n" );
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document.write( "Solution:<BR>\n" );
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document.write( "Number of ways to choose r employees out of n is nCr=n!/(r!(n-r)!).<BR>\n" );
document.write( "(a) <BR>\n" );
document.write( "number of ways to choose 15 out of 200 <BR>\n" );
document.write( "= 15C200<BR>\n" );
document.write( "=14629416353818682834880<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "number of ways to choose 15 out of 144<BR>\n" );
document.write( "= 15C144<BR>\n" );
document.write( "= 85323087086516197776<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "Assuming random selection, probability of choosing 15 non-minority members <BR>\n" );
document.write( "=(15C144)/(15C200)<BR>\n" );
document.write( "= 0.00583  or <0.6%<BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "The probability calculated in (c) does <i>not</i> indicate that the committee selection is biased.  However, if the same selection is repeated many times, the results in (c) would result 1 time out of 171.  Normal interpretation would conclude that it is unlikely that the selection was random.  Usual criteria for cut-off is between 1 in 100 or one in 20. </SPAN>\n" );
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