document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=441696>Question 441696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a multiple choice problem has n possible answers. You guess<BR>\n" );
document.write( "an answer equally likely at random. If you get it wrong, you pick an<BR>\n" );
document.write( "answer equally at random from the remaining choices. You continue<BR>\n" );
document.write( "until you have guessed the right answer, each time only guessing from<BR>\n" );
document.write( "answers you have not tried yet.\r<BR>\n" );
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document.write( "(a) What is the expected number of guesses until you are 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 #304800 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=304800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I won't solve the problem per se for you, because it involves tedious mathematical operating, but I'll tell you the plan of attack:\r<BR>\n" );
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document.write( "Let X = the random variable representing the number of guesses before you get the correct choice.\r<BR>\n" );
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document.write( "Then the pmf (which is a variant of the geometric distribution) is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+%28matrix%282%2C1%2C+n-1%2C+x-1%29%29%2A%28%28n-1%29%2Fn%29%5E%28x-1%29%2A%281%2Fn%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The expectation is then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+E%28X%29+=+sum%28x%2Ap%28x%29%2C+x+=+1%2C+n%29+=+sum%28x%2A%28matrix%282%2C1%2C+n-1%2C+x-1%29%29%2A%28%28n-1%29%2Fn%29%5E%28x-1%29%2A%281%2Fn%29+%2C+x+=+1%2C+n%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Good luck!\r<BR>\n" );
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