document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038464>Question 1038464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine has fifteen identical components that function independently. It will stop working if three or more of the components fail. If the probability that an individual component fails is 0.08, find the probability that the machine will be working<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 #653171 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=653171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if 3 or more of the components fail, then it will stop working.<BR>\n" );
document.write( "that means it will continue working of 0, 1, or 2 of the components fail.<BR>\n" );
document.write( "the probability that an individual component fails is .08.<BR>\n" );
document.write( "the probability that an individual component does not fail is .92.<BR>\n" );
document.write( "this is a binomial probability event with p = .08 and q = .92<BR>\n" );
document.write( "p(x) = c(n,x) * p^x * q^(n-x)<BR>\n" );
document.write( "x is the number of components that will fail.<BR>\n" );
document.write( "p is the probability that an individual component will fail.<BR>\n" );
document.write( "q is the probability that an individual component will not fail.<BR>\n" );
document.write( "n is the total number of components.<BR>\n" );
document.write( "p(x) is the probability that x components will fail.\r<BR>\n" );
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document.write( "the probability that 0 components will fail is p(0) = c(15,0) * .08^0 * .92^15.<BR>\n" );
document.write( "the probability that 1 component will fail is p(1) = c(15,1) * .08^1 * .92^14.<BR>\n" );
document.write( "the probability that 2 components will fail is p(2) = c(15,2) * .08^2 * .92^13.\r<BR>\n" );
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document.write( "you get:<BR>\n" );
document.write( "p(0) = .286297...<BR>\n" );
document.write( "p(1) = .373431...<BR>\n" );
document.write( "p(2) = .227306...<BR>\n" );
document.write( "p(0 + 1 + 2) = .887034...<BR>\n" );
document.write( "this can be rounded off to .8870 which is equal to 88.70%\r<BR>\n" );
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document.write( "this means that the probability of the machine working at any given point in time is 88.70% which means that, in the long run, is should be working 88.70% of the time. </SPAN>\n" );
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