document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=905772>Question 905772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a system of 5 identical units consists of two parts A and B which are connected in series.part A has 2 units connected in parallel and part B has 3 units connected in parallel.all the units function independently with probability of failure 1/2.then the reliability of the system is <BR>\n" );
document.write( "a)31/32<BR>\n" );
document.write( "b)11/32<BR>\n" );
document.write( "c)1/32<BR>\n" );
document.write( "d)21/32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #549381 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=549381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 2 parts.<BR>\n" );
document.write( "they are connected in series.<BR>\n" );
document.write( "any failure in part A or part B will stop the system.<BR>\n" );
document.write( "within part A you have 2 units in parallel.<BR>\n" );
document.write( "for part A to fail both units would have to fail.<BR>\n" );
document.write( "within part B you have 3 units in parallel.<BR>\n" );
document.write( "for part B to fail all 3 units would have to fail.<BR>\n" );
document.write( "your probabilities of failure are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for part A, 1/2 * 1/2 = 1/4 probability that all 2 units will fail at the same time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for part B, 1/2 * 1/2 * 1/2 = 1/8 probability that all 3 units will fail at the same time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that part A will fail is 1/4 and the probability that part B will fail is 1/8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that part A will fail or part B will fail is equal to p(A) + p(B) - p(AB)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the probability that A will fail plus the probability that B will fail minus the probability that both A and B will fail at the same time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get probability of system failure = (1/4) + (1/8) - (1/4) * (1/8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "convert evrything to a denominator of 32 andyou get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(A) + p(B) - p(AB) = 8/32 + 4/32 - 1/32 which becomes 12/32 - 1/32 = 11/32.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that the system will fail completely is 11/32.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the reliability of the system is 1 minus the probability that the system will fail which is equal to 32/32 - 11/32 = 21/32.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that looks like selection d.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );