document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072486>Question 1072486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain college, 33% of the physics majors belong to ethnic minorities. If 8 students are selected at random from the physics majors, what is the probability that more than 5 belong to an ethnic minority?<BR>\n" );
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document.write( "	0.0659<BR>\n" );
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document.write( "	0.9154<BR>\n" );
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document.write( "	0.0187<BR>\n" );
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document.write( "	0.0846<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 #687387 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=687387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this looks like a binomial probability type problem.\r<BR>\n" );
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document.write( "the formula is:\r<BR>\n" );
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document.write( "p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "p is the probability that a student is a minority.<BR>\n" );
document.write( "this makes p = .33\r<BR>\n" );
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document.write( "q is the probability that a student is not a minority.<BR>\n" );
document.write( "this makes q = 1 - .33 = .67\r<BR>\n" );
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document.write( "c(n,x) is the number of ways you can get x minority students out of n students.\r<BR>\n" );
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document.write( "n is the total number of students.\r<BR>\n" );
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document.write( "you have n = 8, p = .33 and q = .67\r<BR>\n" );
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document.write( "c(n,x) is equal to n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "you want to know the probability that more than 5 out of the 8 students will be a minority.\r<BR>\n" );
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document.write( "this means you want to know the probability that 6 or 7 or 8 students out of 8 students is a minority.\r<BR>\n" );
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document.write( "using the formula of p(x) = p^x * q^(n-x) * c(n,x), then you want the sum of:\r<BR>\n" );
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document.write( "p(6) + p(7) + p(8)\r<BR>\n" );
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document.write( "p(6) = .33^6 * .67^2 * c(8,6)<BR>\n" );
document.write( "p(7) = .33^7 * .67^1 * c(8,7)<BR>\n" );
document.write( "p(8) = .33^8 * .67^0 * c(8,8)\r<BR>\n" );
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document.write( "c(8,6) = 8! / (6! * 2!) = 56/2 = 28<BR>\n" );
document.write( "c(8,7) = 8! / (7! * 1!) = 8<BR>\n" );
document.write( "c(8,8) = 8! / (8! * 0!) = 1\r<BR>\n" );
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document.write( "formulas become:\r<BR>\n" );
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document.write( "p(6) = .33^6 * .67^2 * 28 = .016233<BR>\n" );
document.write( "p(7) = .33^7 * .67^1 * 8 = .00228<BR>\n" );
document.write( "p(8) = .33^8 * .67^0 * 1 = .00014\r<BR>\n" );
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document.write( "add these up and round to the 4th decimal place and you get:\r<BR>\n" );
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document.write( "p(6) + p(7) + p(8) = .0187\r<BR>\n" );
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