document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023341>Question 1023341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A multiple choice exam has 12 questions and each question has options a-e to choose from. There is only one correct answer for each question. Assume a student is brought in that has never taken the class, and is just guessing random answers. \r<BR>\n" );
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document.write( "a.) What is the probability he gets them all correct?\r<BR>\n" );
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document.write( "I used the binomial formula: (12!)/(12!-12!) x (.2)^12 x (.8)^0 = 4.096 x 10^-9 \r<BR>\n" );
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document.write( "I dont understand how to make that answer into a percentage/did I do the formula correct for this problem?\r<BR>\n" );
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document.write( "b.) What is the probability that he gets more than 2 correct?<BR>\n" );
document.write( "Do I need to use the binomial formula starting with 3 as k and then do every number as k up to 12? That seems like too much work to do the binomial formula 9 times and then add all those answers up. Is there an easier way to solve for the probability of getting more than 2 correct? <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 #638922 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=638922\">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( "Just like converting any other number to a percentage; you move the decimal point two places to the right.  So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4.096\ \times\ 10^{-9}\ =\ 4.096\ \times\ 10^{-7}%\">\r<BR>\n" );
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document.write( "If you want to calculate the probability of \"more than 2 correct\" straight up, then you are right, you have to calculate the probability of exactly 3 plus the probability of exactly 4, plus...and so on all the way up to 12.  However, the probability of MORE THAN 2 is equal to 1 minus the probability of 2 OR LESS.  Calculate the probability of 0, 1, and 2, add the three probabilities, and subtract from 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_{12}(\geq 3,0.2)\ =\ \sum_{k\ =\ 3}^{12}{{12}\choose{k}}\left(0.2\right)^k\left(0.8\right)^{12\,-\,k}\ =\ 1\ -\ P_{12}(< 3,0.2)\ =\ 1\ -\ \sum_{k\ =\ 0}^{2}{{12}\choose{k}}\left(0.2\right)^k\left(0.8\right)^{12\,-\,k}\">\r<BR>\n" );
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document.write( "If you have either Excel (on a Windows machine) or Numbers (on a Mac), open a spreadsheet and enter\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ =BINOMDIST(3,12,0.2,TRUE)\">\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" );
document.write( "My calculator said it, I believe it, that settles it\r<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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