document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=851027>Question 851027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The classification of faculty at a college is indicated in the following table:\r<BR>\n" );
document.write( "\n" );
document.write( "	Male	Female	Total <BR>\n" );
document.write( "Professor	12	3	15<BR>\n" );
document.write( "Associate professor	15	9	24<BR>\n" );
document.write( "Assistant professor 	18	8	26<BR>\n" );
document.write( "Instructor	20	15	35<BR>\n" );
document.write( "Total	65	35	100\r<BR>\n" );
document.write( "\n" );
document.write( "a)	If  a committee of three faculty members is selected at random what is the probability that:<BR>\n" );
document.write( "i)	All females.<BR>\n" );
document.write( "ii)	A professor and two associate professor .<BR>\n" );
document.write( "b)	 If a faculty member is selected at random from this college, find the probability that:<BR>\n" );
document.write( "i)	The faculty is male, given that the faculty is instructor.<BR>\n" );
document.write( "ii)	The faculty is not professor given that the faculty is female.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #512520 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=512520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The classification of faculty at a college is indicated in the following table:\r<BR>\n" );
document.write( "\n" );
document.write( ".........................Male	Female	Total <BR>\n" );
document.write( "Professor................12	3	15<BR>\n" );
document.write( "Associate professor......15	9	24<BR>\n" );
document.write( "Assistant professor.....	18	8	26<BR>\n" );
document.write( "Instructor........	20	15	35<BR>\n" );
document.write( "Total.............	65	35	100\r<BR>\n" );
document.write( "\n" );
document.write( "a) If  a committee of three faculty members is selected at random what is the probability that:<BR>\n" );
document.write( "i) All females.:: <BR>\n" );
document.write( "# of ways to select 3 female faculty members:: 35C3 <BR>\n" );
document.write( "# pf ways to select 3 random faculty members:: 100C3<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Ans:: 35C3/100C3 = 0.0405<BR>\n" );
document.write( "ii) A professor and two associate professor <BR>\n" );
document.write( "# of ways to select a professor (15) and 2 assoc. profs (24C2)::<BR>\n" );
document.write( "# of ways to select 3 random faculty members:: 100C3<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Ans::  [15*24C2]/100C3 = 0.0256<BR>\n" );
document.write( "b) If a faculty member is selected at random from this college, find the probability that:<BR>\n" );
document.write( "i) The faculty is male, given that the faculty is instructor. <BR>\n" );
document.write( "Ans:: (# of ways to succeed)/(# of random selection) = 20/35<BR>\n" );
document.write( "ii)The faculty is not professor given that the faculty is female<BR>\n" );
document.write( "Ans:: (# of ways to succeed)/(# of random selections) =  32/35<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );