document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=326205>Question 326205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone tell me if I worked this problem right?  A committee of two is selected at random from a set consisting of three Democrats, four Republicans and one Independent.\r<BR>\n" );
document.write( "\n" );
document.write( "(a)What is the probability that the committee consists of no Republicans?  <BR>\n" );
document.write( "      I count the combination's of not getting an R;  so I have d1,d2,d3,I  to select from. I can have d1,d2 - d1,d3 - d1,I - d2,d3 – d2,I – d3,I              6 combo’s <BR>\n" );
document.write( "Six chances to pull 2 (or one of those combinations) I take the median: <BR>\n" );
document.write( "8*7*6/ 1*2*3 = 56    so I’ve got 6/56   or 3/28\r<BR>\n" );
document.write( "\n" );
document.write( "(b) What is the probability that the committee consists of all Republicans?<BR>\n" );
document.write( "Combo’s r1, r2, r3, r4: r1,r2 – r1,r3 – r1,r4 – r2,r3 – r2,r4 – r3,r4 	        6 combo’s again so the chances are the same.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233494 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(a) There is a pool of 8 people to choose from, and 4 of them are not Republicans.  So the probability that the first person chosen will not be a Republican is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{4}{8}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once the first person is chosen and it is, in fact, not a Republican, then you now have a pool of 7 people from which to choose, 3 of which are not Republicans.  So the probability that the second person chosen will not be a Republican given that the first was not a Republican is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{3}{7}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The total probability is the product: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\frac{4}{8}\right)\left(\frac{3}{7}\right)\ =\ \frac{12}{56}\ =\ \frac{3}{14}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b) There is a pool of 8 people to choose from, and 4 of them are  Republicans.  So the probability that the first person chosen will be a Republican is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{4}{8}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once the first person is chosen and it is, in fact, a Republican, then you now have a pool of 7 people from which to choose, 3 of which are Republicans.  So the probability that the second person chosen will be a Republican given that the first was a Republican is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{3}{7}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The total probability is the product: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\frac{4}{8}\right)\left(\frac{3}{7}\right)\ =\ \frac{12}{56}\ =\ \frac{3}{14}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );