document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258309>Question 258309</A>: <I><SPAN STYLE=\"word-break: break-all;\">   Airlines  find  that each passenger who  reserves a seat fails  to  turn up with probability  1/10  independently of the other passengers.  So Teeny Weeny Airlines  always  sell  10  tickets  for  their 9  seat aeroplane while Blockbuster Airways always sell 20 tickets for their 18 seat aeroplane. Which is more often over-booked?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190150 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=190150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probability that a passenger will not show up 10% of the time means the passenger will show up 90% of the time.\r<BR>\n" );
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document.write( "any plane is overbooked when at least one passenger is denied.\r<BR>\n" );
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document.write( "for the smaller plane this happens when all 10 passengers show up for the 9 seats.\r<BR>\n" );
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document.write( "the probability of this happening is .9^10 = .34867844.\r<BR>\n" );
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document.write( "for the larger plan this happens when all 20 passengers show up or when 19 of the 20 passengers show up for the 18 seats.\r<BR>\n" );
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document.write( "probability of all 20 passengers showing up for the larger plane is .9^20 = .121576655.\r<BR>\n" );
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document.write( "probability that exactly 19 passengers show up for the larger plane is .1^1 * .9^19 * C(20,1).\r<BR>\n" );
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document.write( "C(20,1) is the number of possible combinations of selecting 1 out of 20.\r<BR>\n" );
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document.write( "C(20,1) = 20!/(19!*1!) = (20*19!)/19! = 20\r<BR>\n" );
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document.write( "proability that exactly 19 passengers will show up for the larger plane is therefore .1^1 * .9^19 * 20 = .270170344.\r<BR>\n" );
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document.write( "probability that all 18 passengers or exactly 19 passengers will show up for the larger plane is equal to .121576655 + .270170344 = .391746998\r<BR>\n" );
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document.write( "based on the probabilities, the larger plane should be overbooked more often than the smaller plane.\r<BR>\n" );
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