document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=590337>Question 590337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> probability of failure of compnent is 0.06. Than what is the probability of failure of 109 components<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 #375155 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=375155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the probability of failure of one component is .06, then the probability of success of one component is 1 - .06 = .97<BR>\n" );
document.write( "if you take a sample of n components, then the formula for the number of failures in that sample would be:<BR>\n" );
document.write( "p(x failures) = C(n,x) * p^x * q^(n-x)<BR>\n" );
document.write( "C(n,x) equals the combination formula of n! / (x! * (n-x)!)<BR>\n" );
document.write( "p^x equals the probability of failure raised to the power of x.<BR>\n" );
document.write( "q^(n-x) equals the probability of success raised to the power of (n-x).<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "you draw a sample of 3 components.<BR>\n" );
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document.write( "p(0 failures) = C(3,0) * .06^0 * .94^3 which equals .830584\r\n" );
document.write( "p(1 failure)  = C(3,1) * .06^1 * .94^2 which equals .159048\r\n" );
document.write( "p(2 failures) = C(3,2) * .06^2 * .94^1 which equals .010152\r\n" );
document.write( "p(3 failures) = C(3,3) * .06^3 * .94^0 which equals .000216\r\n" );
document.write( "total of all possible probabilities is equal to:    1.00000\r\n" );
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document.write( "the sum of all probabilities is equal to 1 as it should be.\r<BR>\n" );
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document.write( "if you draw a sample of 1000 components, then the sum of all probabilities will still be equal to 1 but each possible probability will be much less.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "the probability of exactly 106 defective components out of the sample of 1000 components is equal to:<BR>\n" );
document.write( "C(1000,106) * .06^106 * .97^894 which is equal to ?????<BR>\n" );
document.write( "my calculator is unable to calculate this.<BR>\n" );
document.write( "it tells me that C(100,106) is too large for it to  handle (overflow error).<BR>\n" );
document.write( "it tells me that .06^106 is equal to 0.<BR>\n" );
document.write( "it tells me that .94^894 is equal to 9.468934625 * 10^(-25)\r<BR>\n" );
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document.write( "suffice it to say that the probability of getting 106 defective components out of a batch of 1000 components is extremely small.\r<BR>\n" );
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document.write( "try something like 50 failures out of a batch of 100 components.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "p(50 failures) = C(100,50) * .06^50 * .94^50 which is equal to 3.696656602 * 10^(-34)<BR>\n" );
document.write( "that's a very small number.\r<BR>\n" );
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