document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130974>Question 1130974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A multiple-choice test contains 12 questions, each with four answers. Assume a student just guesses on each question.\r<BR>\n" );
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document.write( "(Please enter your answers as fractions in simplest form or as decimals rounded to four decimal places. Thank you!)\r<BR>\n" );
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document.write( "a. What is the probability that the student answers more than five questions correctly?\r<BR>\n" );
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document.write( "b. What is the probability that the student answers less than four questions correctly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747665 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=747665\">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 <i>exactly</i> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials 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 <i>at least</i> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials 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( "The probability of <i>at most</i> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials 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(\leq{k},n,p)\ =\ \sum_{r=0}^k\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n-r}\">\r<BR>\n" );
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document.write( "Your number of trials is 12, and the probability of success on any trial is 1 in 4 or 0.25.  Note that \"more than 5\" is the same as \"at least 6\", and \"less than 4\" is the same as \"at most 3\".  You can do your own arithmetic.<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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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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