document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127552>Question 1127552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a student takes a 22 question multiple choice exam with four choices for each question and guesses on each question. Assume the variable is binomial find the probability of guessing at least 7 out of 22 correctly </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743964 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=743964\">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( "You need the probability of seven successes out of 22 trials, plus eight successes out of 22 trials, plus nine...and so on up to 22 successes out of 22 trials.\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 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( "So you need the sum:\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( "For at least 7 out of 22, you will have a sum with 16 terms.  The following sum, which gives you the same result only requires calculating 8 terms:\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\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n\,-\,r}\">\r<BR>\n" );
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document.write( "Make sure your calculator has fresh batteries.<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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