document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134959>Question 1134959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small regional carrier accepted 16 reservations for a particular flight with 12 seats. 8 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 48% chance, independently of each other. \r<BR>\n" );
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document.write( "A) Find the probability that overbooking occurs. <BR>\n" );
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document.write( "B) Find the probability that the flight has empty seats. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752478 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> empty seats mean that no more than 3 of the other 8 will arrive for the flight.<BR>\n" );
document.write( "probability of 3 arriving is 8C3*0.48^3*0.52^5=0.2355<BR>\n" );
document.write( "probability of 2 arriving is then 0.1275<BR>\n" );
document.write( "probability of 1 is 0.0395<BR>\n" );
document.write( "probability of 0 is 0.0053<BR>\n" );
document.write( "That sum is 0.4078 ANSWER B<BR>\n" );
document.write( "overbooking is 5,6,7,8.<BR>\n" );
document.write( "do just 4, even though this isn't asked for <BR>\n" );
document.write( "probability is 70*0.48^4*0.52^4=0.2717<BR>\n" );
document.write( "This plus the 0.4078 is 0.6795\r<BR>\n" );
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document.write( "That is the probability no overbooking will occur.  The probability that overbooking will occur is the complement of 0.3205 ANWER A </SPAN>\n" );
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