document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025954>Question 1025954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company intends to form its CSR committee with 4 members, from a pool of 14 managers (5 women and 9 men). <BR>\n" );
document.write( "A) What is the probability that all members of the CSR committee would be female managers?<BR>\n" );
document.write( "B) What is the probability that all members of the CSR committee would be male managers?<BR>\n" );
document.write( "C) What is the probability of having at least 3 female managers in the CSR committee?<BR>\n" );
document.write( "D) How many male managers should be removed from the pool so that board of directors can be 90% confident of having at least half of the CSR commitee represented by female managers?<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 #641247 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=641247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the formulas will be:\r<BR>\n" );
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document.write( "formula 1.<BR>\n" );
document.write( "p(exactly 4 women) = 5c4 / 14c4 = .004995...\r<BR>\n" );
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document.write( "formula 2.<BR>\n" );
document.write( "p(exactly 4 men) = 9c4 / 14c4 = .125874...\r<BR>\n" );
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document.write( "formula 3.<BR>\n" );
document.write( "p(exactly 3 women) = (5c3 * 9c1) / 14c4 = .089910...\r<BR>\n" );
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document.write( "formula 4.<BR>\n" );
document.write( "p(at least 3 women) = p(exactly 3 women) + p(exactly 4 women) = formula 3 plus formula 1 = .089910... + .004995... = .094905...\r<BR>\n" );
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document.write( "this can be seen in the worksheet by adding up the cells F8 and F9.<BR>\n" );
document.write( "F8 is column F row 8.<BR>\n" );
document.write( "F9 is column F row 9.\r<BR>\n" );
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document.write( "in order for the probability to be equal to or greater than 90% that there will be at least 2 women on the team, then the number of men has to be reduced to 3.\r<BR>\n" );
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document.write( "this means that 6 of the men must be removed from the pool.\r<BR>\n" );
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document.write( "when there are only 3 men in the pool, then the probability that the team will consist of all men becomes equal to 0 because the team requires 4 members and there are only 3 men available.\r<BR>\n" );
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document.write( "the following worksheet summarizes the calculations.\r<BR>\n" );
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document.write( "the worked up probabilities are in the worksheet.\r<BR>\n" );
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document.write( "p(0 women) means p(4 men)<BR>\n" );
document.write( "p(1 woman) means p(1 woman and 3 men).<BR>\n" );
document.write( "p(2 women) means p(2 women and 2 men).<BR>\n" );
document.write( "p(3 women) means p(3 women and 1 man).<BR>\n" );
document.write( "p(4 women) means p(4 women and 0 men).\r<BR>\n" );
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document.write( "column F contains the results for 5 women and 9 men, shown as 5w9m.\r<BR>\n" );
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document.write( "the other columns follow the same convention.\r<BR>\n" );
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document.write( "5w8m means 5 women and 8 men, etc.\r<BR>\n" );
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document.write( "here's the worksheet.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/032101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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