document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=671680>Question 671680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Airlines sell more tickets for a flight than the number of available seats (overbooking).  They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.   \r<BR>\n" );
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document.write( "(a)  A plane has 6 seats.  If the airline sells 8 tickets for a flight, what is the probability that the flight will be overbooked (the number of passengers who show up is greater than the number of available seats)?\r<BR>\n" );
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document.write( "(b)  A plane has 325 seats.  If the airline sells 350 tickets for a flight, what is the probability that the flight will be overbooked (the number of passengers who show up is greater than the number of available seats)?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417513 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let p (not showing) = .10  \r<BR>\n" );
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document.write( "1) Let n = 8. This situation satisfies the binomial distribution.\r<BR>\n" );
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document.write( "Choose 0 to not show up:\r<BR>\n" );
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document.write( "(8 choose 0) (.1)^0 (.9)^8\r<BR>\n" );
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document.write( "Choose 1 to not show up:\r<BR>\n" );
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document.write( "(8 choose 1) (.1)^1 (.9)^7\r<BR>\n" );
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document.write( "Adding this we get:\r<BR>\n" );
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document.write( "(.9)^8 + 8 * .1 * .9^7 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28.8131%29 ALIGN=MIDDLE  ALT=\"highlight%28.8131%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) Let n = 350 \r<BR>\n" );
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document.write( "In the same way:\r<BR>\n" );
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document.write( "(350 choose 0) *(.1)^0 (.9)^349 + (350 choose 1) * (.1)^1 (.9)^348 + ... + (350 choose 24) *(.1)^24 (.9)^326 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28.0261%29 ALIGN=MIDDLE  ALT=\"highlight%28.0261%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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