document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=841689>Question 841689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A statistics textbook chapter contains 66 exercises, 12 of which are essay questions. A student is assigned 16 problems. What is the probability that at least one is essay?<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 #507127 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=507127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "A statistics textbook chapter contains 66 exercises, 12 of which are essay questions. A student is assigned 16 problems. What is the probability that at least one is essay?<BR>\n" );
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document.write( "A:<BR>\n" );
document.write( "If we use Binomial Distribution, we only get an approximate answer since the probability of success (the event of answering an essay question) is different from trial to trial.<BR>\n" );
document.write( "We use Hypergeometric Distribution to get the exact answer.<BR>\n" );
document.write( "P(none are essay) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C12%2C0%29%29%28matrix%282%2C1%2C54%2C16%29%29%2F%28%28matrix%282%2C1%2C66%2C16%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.02466<BR>\n" );
document.write( "Therefore, P(at least one essay) = 1 - 0.02466 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.97534%29 ALIGN=MIDDLE  ALT=\"highlight%280.97534%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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