document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995872>Question 995872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that of 100 computers checked for viruses 30 where infected and 70 where not. If we select 10 computers at random what is the probability that at most 4 of them are infected </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614525 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=614525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability that at most 4 of them are infected is equal to the probability that 0 of them are infected plus 1 of them are infected plus 2 of them are infected + 3 of them are infected + 4 of them are infected.\r<BR>\n" );
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document.write( "this uses the binomial probability formula which is:\r<BR>\n" );
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document.write( "p(x) = nCx * p^x * q^(n-x)\r<BR>\n" );
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document.write( "p is the probability of infected which is 30 / 100 = .3<BR>\n" );
document.write( "q is the probability of not infected which is 1 - .3 = .7\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "the probability that exactly 1 out of the 10 will fail is 10C1 * .3^1 * .7^9.\r<BR>\n" );
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document.write( "p(1) is therefore equal to 10 * .3 * .040353607 = .121060821.\r<BR>\n" );
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document.write( "the sum of all the probabilities must be equal to 1 or you did something wrong.\r<BR>\n" );
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document.write( "here's the probabilities for all the possibilities.\r<BR>\n" );
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document.write( "in this spreadsheet p*(3) whould really have been just p(3).<BR>\n" );
document.write( "the * is a typo.<BR>\n" );
document.write( "my keyboard likes to add extra characters sometimes and i don't always catch it before publishing.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/101201.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's a reference on how to use the binomial probability formula.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://regentsprep.org/regents/math/algtrig/ATS7/BLesson.htm\" target = \"_blank\">http://regentsprep.org/regents/math/algtrig/ATS7/BLesson.htm</a>\r<BR>\n" );
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document.write( "the combination formula can be referenced as nCx, C(n,x) or the form that is shown in the reference.\r<BR>\n" );
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