document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161643>Question 1161643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every day, there is a 90% chance that Kevin will spill coffee on himself while driving to work.\r<BR>\n" );
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document.write( "Looking at the next eight days, what is the probability that Kevin will spill coffee on himself on just two of those days? \r<BR>\n" );
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document.write( "Looking at the next eight days, what is the probability that Kevin will spill coffee on himself on at least two of those days?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785250 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5347)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each day Kevin drives to work,<BR>\n" );
document.write( "there is a 90% chance (p=0.9) that Kevin will spill coffee on himself while driving, and<BR>\n" );
document.write( "there is a 100%-90%=10% chance (p=1-0.9=0.1) that Kevin will not spill coffee on himself while driving.<BR>\n" );
document.write( "If you consider one day that Kevin drives to work, the binomial<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.9s%2B0.1n%29 ALIGN=MIDDLE  ALT=\"%280.9s%2B0.1n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents that p=1 possibility that one or another of the possible outcomes will happen.<BR>\n" );
document.write( "The coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9 ALIGN=MIDDLE  ALT=\"0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > in front of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for spill) represents the possibility that Kevin will spill coffee on himself.<BR>\n" );
document.write( "The coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1 ALIGN=MIDDLE  ALT=\"0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in front of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for no spill) represents the possibility that Kevin will not spill coffee on himself.<BR>\n" );
document.write( "considering multiple days, the possibilities multiply.<BR>\n" );
document.write( "If you consider <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > days that Kevin drives to work, the power of a binomial<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.9s%2B0.1n%29%5E8 ALIGN=MIDDLE  ALT=\"%280.9s%2B0.1n%29%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9%5E8s%5E8%2B8%280.9%5E7s%5E7%29%280.1n%29%2B28%280.9%5E6s%5E6%29%280.1%5E2n%5E2%29%2B%22...%22%2B28%280.9%5E2s%5E2%29%280.1%5E6n%5E6%29%2B8%280.9s%29%280.1%5E7s%5E7%29%2B0.1%5E8s%5E8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "represent the probability that one or another of the many outcomes possible will happen.<BR>\n" );
document.write( "The coefficient of the term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%280.9%5E2s%5E2%29%280.1%5E6n%5E6%29=28%280.9%5E2%29%280.1%5E6%29s%5E2n%5E6 ALIGN=MIDDLE  ALT=\"28%280.9%5E2s%5E2%29%280.1%5E6n%5E6%29=28%280.9%5E2%29%280.1%5E6%29s%5E2n%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "represents the possibility that<BR>\n" );
document.write( "Kevin will spill coffee on himself on 2 of those days,<BR>\n" );
document.write( "but will not spill coffee on himself on the other 6 days.<BR>\n" );
document.write( "That is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%280.9%5E2%29%280.1%5E6%29=28%2A0.81%2A0.000001=0.00000081 ALIGN=MIDDLE  ALT=\"28%280.9%5E2%29%280.1%5E6%29=28%2A0.81%2A0.000001=0.00000081\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%280.9%5E2%29%28%2810%5E-1%29%5E6%29=28%2A0.81%2A10%5E-6=%288.1%2A10%5E-1%29%2A10%5E-6=8.1%2A10%5E-7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The possibility that Kevin will not spill coffee on himself while driving on any of those 8 days is the coefficient o the term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%5E8n%5E8 ALIGN=MIDDLE  ALT=\"0.1%5E8n%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%5E8=1%2A10%5E-0.1%2A10%5E-7 ALIGN=MIDDLE  ALT=\"0.1%5E8=1%2A10%5E-0.1%2A10%5E-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.00000001 ALIGN=MIDDLE  ALT=\"0.00000001\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The possibility that Kevin will spill coffee on himself while driving only 1 of those 8 days is the coefficient o the term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%280.9s%29%280.1%5E7s%5E7%29=8%2A0.9%2A0.1%5E7sn%5E7 ALIGN=MIDDLE  ALT=\"8%280.9s%29%280.1%5E7s%5E7%29=8%2A0.9%2A0.1%5E7sn%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A0.9%2A0.1%5E7=7.2%2A10-7 ALIGN=MIDDLE  ALT=\"8%2A0.9%2A0.1%5E7=7.2%2A10-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.00000072 ALIGN=MIDDLE  ALT=\"0.00000072\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Adding those two possibilities,<BR>\n" );
document.write( "the possibility that Kevin will sill coffe on himself on no more than 1 of those 8 days is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.2%2A10%5E-7%2B0.1%2A10%5E-7=7.3%2A10%5E-7 ALIGN=MIDDLE  ALT=\"7.2%2A10%5E-7%2B0.1%2A10%5E-7=7.3%2A10%5E-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.00000072%2B0.00000001=0.00000073 ALIGN=MIDDLE  ALT=\"0.00000072%2B0.00000001=0.00000073\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The possibility of the opposite (Kevin spilling coffee on himself at least 2 of the 8 days is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.00000073=0.99999927 ALIGN=MIDDLE  ALT=\"1-0.00000073=0.99999927\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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