document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172912>Question 1172912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. Among the applicants to two vacant positions, three males and two female applicants<BR>\n" );
document.write( "qualify for the final interview. Because of scheduling problems, only two applicants can<BR>\n" );
document.write( "be interviewed immediately. The personnel manager selects these two be assigning a<BR>\n" );
document.write( "numbered colored ticket to each applicant (say B1 and R1 for 1st male applicant in Blue<BR>\n" );
document.write( "ticket and 1st female applicant in Red ticket, respectively), and then randomly drawing<BR>\n" );
document.write( "two tickets.<BR>\n" );
document.write( "(a) What is the sample space for this experiment?<BR>\n" );
document.write( "(b) what is the event that at least one male is interviewed immediately? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850798 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely, let's break down this probability problem step-by-step.\r<BR>\n" );
document.write( "\n" );
document.write( "**a. Sample Space**\r<BR>\n" );
document.write( "\n" );
document.write( "First, let's assign labels to the applicants:\r<BR>\n" );
document.write( "\n" );
document.write( "* Males: B1, B2, B3 (Blue tickets)<BR>\n" );
document.write( "* Females: R1, R2 (Red tickets)\r<BR>\n" );
document.write( "\n" );
document.write( "We need to find all possible pairs of applicants that can be interviewed. We can list them systematically:\r<BR>\n" );
document.write( "\n" );
document.write( "* B1, B2<BR>\n" );
document.write( "* B1, B3<BR>\n" );
document.write( "* B1, R1<BR>\n" );
document.write( "* B1, R2<BR>\n" );
document.write( "* B2, B3<BR>\n" );
document.write( "* B2, R1<BR>\n" );
document.write( "* B2, R2<BR>\n" );
document.write( "* B3, R1<BR>\n" );
document.write( "* B3, R2<BR>\n" );
document.write( "* R1, R2\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the sample space (S) is:\r<BR>\n" );
document.write( "\n" );
document.write( "S = { (B1, B2), (B1, B3), (B1, R1), (B1, R2), (B2, B3), (B2, R1), (B2, R2), (B3, R1), (B3, R2), (R1, R2) }\r<BR>\n" );
document.write( "\n" );
document.write( "**b. Event: At Least One Male is Interviewed**\r<BR>\n" );
document.write( "\n" );
document.write( "Let's identify the outcomes in the sample space where at least one male is interviewed:\r<BR>\n" );
document.write( "\n" );
document.write( "* (B1, B2)<BR>\n" );
document.write( "* (B1, B3)<BR>\n" );
document.write( "* (B1, R1)<BR>\n" );
document.write( "* (B1, R2)<BR>\n" );
document.write( "* (B2, B3)<BR>\n" );
document.write( "* (B2, R1)<BR>\n" );
document.write( "* (B2, R2)<BR>\n" );
document.write( "* (B3, R1)<BR>\n" );
document.write( "* (B3, R2)\r<BR>\n" );
document.write( "\n" );
document.write( "Let's call this event \"M\".\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore:\r<BR>\n" );
document.write( "\n" );
document.write( "M = { (B1, B2), (B1, B3), (B1, R1), (B1, R2), (B2, B3), (B2, R1), (B2, R2), (B3, R1), (B3, R2) }<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );