document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147272>Question 1147272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A senate committee of five members is to be selected from N Labor and five Liberal senators. Use trial and error to find the minimum value of N, given that the probability of Labor having a majority on the committee is greater than 3/4 . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #768620 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=768620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem specifically asks you to use trial and error to find the answer.  We can't help you with that....<br><BR>\n" );
document.write( "If the number of Labor senators is x, then the probability of having a majority of labor senators on the 5-member committee (that is, 3 or 4 o 5 labor senators out of the 5 total) is<br><BR>\n" );
document.write( "({x choose 3) times (5 choose 2)) plus ((x choose 4) times (5 choose 1)) plus ((x choose 5) times (5 choose 0)), and then all that divided by ((x+5) choose 5).<br><BR>\n" );
document.write( "Plug in values of x until you find the smallest value that makes the probability greater than 0.75.<br><BR>\n" );
document.write( "It should make sense to you that if x=5 (the number of Labor and Liberal senators is the same), then there is an equal probability for either party to have a majority on the 5-member committee; so the answer is going to be a number greater than 5.<br><BR>\n" );
document.write( "If you have a good graphing calculator, you can make it do nearly all the work for you.  On my TI-83 I am able to enter the complete expression shown above as a function; I couldn't get it to graph the function, but the TABLE option made it easy to quickly see the answer to the question. </SPAN>\n" );
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