document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=400430>Question 400430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose there are 35 students in a class and 30 lectures in 1 semester.  If 4 students are randomly picked in a class to answer questions, what is the probability that one student is never called during the semester?\r<BR>\n" );
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document.write( "I would say almost 0% but I don't know where to begin. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #283441 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=283441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2834C4%29%2F%2835C4%29%29%5E30+=+%2831%2F35%29%5E30+=+0.02623 ALIGN=MIDDLE  ALT=\"%28%2834C4%29%2F%2835C4%29%29%5E30+=+%2831%2F35%29%5E30+=+0.02623\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to 5 decimal places.\r<BR>\n" );
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document.write( "To explain the answer, consider excluding student A, e.g., from the class of 35.  Then there are 34C4 possible ways of selecting groups of 4 students from the remaining 34 students. <BR>\n" );
document.write( "The total number of groups of 4 students coming from the entire class of 35 is 35C4 (regardless whether person A is included or not.)<BR>\n" );
document.write( "Hence in a particular lecture, the probability of person A not being included in the group of 4 students is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2834C4%29%2F%2835C4%29+=+31%2F35 ALIGN=MIDDLE  ALT=\"%2834C4%29%2F%2835C4%29+=+31%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Since the event of student A not being called in any of the 30 lectures is identically and independently copied for all 30 lectures, the probability is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2834C4%29%2F%2835C4%29%29%5E30+=+%2831%2F35%29%5E30 ALIGN=MIDDLE  ALT=\"%28%2834C4%29%2F%2835C4%29%29%5E30+=+%2831%2F35%29%5E30\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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