document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=829781>Question 829781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a home theater system, the probability that the video components need repair within 1 year is 0.01, the probability that the electronic components need repair within 1 year is 0.006, and the probability that the audio components need repair within 1 year is 0.004. Assuming that the events are independent, find the following probabilities. (Round your answers to four decimal places.)<BR>\n" );
document.write( "(a) At least one of these components will need repair within 1 year=<BR>\n" );
document.write( "(b) Exactly one of these component will need repair within 1 year= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #500098 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=500098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a home theater system, the probability that the video components need repair within 1 year is 0.01, the probability that the electronic components need repair within 1 year is 0.006, and the probability that the audio components need repair within 1 year is 0.004. Assuming that the events are independent, find the following probabilities. (Round your answers to four decimal places.)\r<BR>\n" );
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document.write( "(a) At least one of these components will need repair within 1 year=<BR>\n" );
document.write( "    probability = 1 - (1 - 0.01)(1 - 0.006)(1 - 0.004) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.0199%29 ALIGN=MIDDLE  ALT=\"highlight%280.0199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) Exactly one of these component will need repair within 1 year=<BR>\n" );
document.write( "    probability <BR>\n" );
document.write( "=0.01(1-0.006)(1-.004)+(1-0.01)(0.006)(1-.004)+(1-0.01)(1-0.006)(.004) <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.0198%29 ALIGN=MIDDLE  ALT=\"highlight%280.0198%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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