document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130879>Question 1130879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What type of problem is this and how do I solve it?\r<BR>\n" );
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document.write( "If 15 of the students from the special programs are randomly selected, find the probability that 12 of them graduated (84% for students admitted through special programs).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747538 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 15 students from the special program are selected.<BR>\n" );
document.write( "84.<BR>\n" );
document.write( "the probability that a student from the special program graduates is 84% = .84<BR>\n" );
document.write( "you want to find the probability that 12 of them graduated.\r<BR>\n" );
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document.write( "looks like a binomial probability type problem.\r<BR>\n" );
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document.write( "equation for that is p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "in this problem, that becomes:\r<BR>\n" );
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document.write( "p(12) = .84 ^ 12 * (1 - .84) ^ 15 - 12) * c(15,12)\r<BR>\n" );
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document.write( ".84 is the probability that a student from the special program will graduate.<BR>\n" );
document.write( "1 - .84 = .16 is the probability that a student from the special program will not graduate.<BR>\n" );
document.write( "c(15,12) = the number of ways you can get a set of 12 elements from a set of 15 elements = 15! / (12! * 3!) = 455\r<BR>\n" );
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document.write( "the formula becomes .84 ^ 12 * .16 ^ 3 * 455 = .229997321.\r<BR>\n" );
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document.write( "i checked out all the probabilities using excel.<BR>\n" );
document.write( "the total probability is 1 as it should be.<BR>\n" );
document.write( "here's a display of what excel showed me.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/120401.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "look at the row where x = 12 and you'll see that p(x) equals 0.229997321 which is the same as i got manually using my scientific calculator.\r<BR>\n" );
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document.write( "that is the probability that exactly 12 of them graduated if you picked those 12 out of 15 randomly selected student in the special program.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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