document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274425>Question 274425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent. If someone burglarizes your home, what is the probability that <BR>\n" );
document.write( "(a) both components fail? <BR>\n" );
document.write( "(b) at least one component functions properly?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200267 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=200267\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent. If someone burglarizes your home, what is the probability that <BR>\n" );
document.write( "(a) both components fail?: 0.9*0.7 = 0.63<BR>\n" );
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document.write( "(b) at least one component functions properly?<BR>\n" );
document.write( "P(at least one) = 1 - P(both fail) = 1-0.63 = 0.37<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );