document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281485>Question 281485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You flip a coin 10 times.What is the P(8H)?What is the P(>8H)?<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 #204488 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=204488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" 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\"> successes out of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is the probability of success on any given trial is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_n(k)\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(n\cr k\right)\"> is the number of ways to select <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> things out of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things and is equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n!}{k!(n\,-\,k)!}\">.\r<BR>\n" );
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document.write( "So for the first part of your question, you need to calculate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_{10}(8)\ =\ \left(10\cr \,8\right\)\left(\frac{1}{2}\right)^8\left(\frac{1}{2}\right)^{2}\">\r<BR>\n" );
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document.write( "Because you want the probability of 8 heads in 10 flips where the probability of getting heads is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{2}\">\r<BR>\n" );
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document.write( "The probability of <b><i>more than</i></b> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes out of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is the probability of success on any given trial is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_n(> k)\ =\ \sum_{i=k\,+\,1}^n\left(\left(n\cr i\right\)p^i\left(1\,-\,p\right)^{n\,-\,i}\right)\">\r<BR>\n" );
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document.write( "So, you need to calculate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_{10}(> 8)\ =\ P_{10}(9)\ +\ P_{10}(10)\ =\  \left(10\cr \,9\right\)\left(\frac{1}{2}\right)^9\left(\frac{1}{2}\right)^{1}\ +\  \left(10\cr \,10\right\)\left(\frac{1}{2}\right)^{10}\left(\frac{1}{2}\right)^{0}\">\r<BR>\n" );
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document.write( "Use MS Excel to check your work.  Pick any cell on a blank worksheet and type in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{=BINOMDIST(8,10,0.5,FALSE)}\">\r<BR>\n" );
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document.write( "for the first part and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{=1-BINOMDIST(8,10,0.5,TRUE)}\">\r<BR>\n" );
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document.write( "for the second part.\r<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" );
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