document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124881>Question 1124881</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 five days, what is the probability that Kevin will spill coffee on himself on just two of those days? <BR>\n" );
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document.write( "Looking at the next five days, what is the probability that Kevin will spill coffee on himself on at least two of those days? <BR>\n" );
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document.write( "Enter your answers as whole numbers or decimals.\r<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 #741194 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The probability of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successful outcomes of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> experiments where the probability of success on any given trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(k,n,p)\ =\  {{n}\choose{k}}\(p\)^k\(1\,-\,p\)^{n\,-\,k}\">\r<BR>\n" );
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document.write( "The probability of <u>at least</u> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successful outcomes of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> experiments where the probability of success on any given trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(\geq{k},n,p)\ =\  \sum_{r=k}^n\,{{n}\choose{r}}\(p\)^r\(1\,-\,p\)^{n\,-\,r}\">\r<BR>\n" );
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document.write( "Although it may be more convenient to calculate the equivalent expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(\geq{k},n,p)\ =\  1\ -\ P(<k,n,p)\ =\ 1 - \sum_{r=0}^{k-1}\,{{n}\choose{r}}\(p\)^r\(1\,-\,p\)^{n\,-\,r}\">\r<BR>\n" );
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document.write( "All you need to do is plug in your given numbers and do the arithmetic.  In the case of your specific problem, the \"equivalent expression\" will be much simpler to calculate for your second problem.  Don't forget that the probability must be expressed as a decimal.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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