document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187583>Question 1187583</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A box contains 1000 light bulbs. The probability that there is at least 1 defective bulb<BR>\n" );
document.write( "in the box is 0.1, and the probability that there are at least 2 defective bulbs is 0.05.<BR>\n" );
document.write( "Find the probability in each of the following cases:<BR>\n" );
document.write( "(a) The box contains no defective bulbs.<BR>\n" );
document.write( "(b) The box contains exactly 1 defective bulb.<BR>\n" );
document.write( "(c) The box contains at most 1 defective bulb. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819196 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability that there are no defective bulbs is 0.9, since the rest of the probability (0.1) is devoted to 1 or more defective bulbs.<BR>\n" );
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document.write( "that means that the probability of a bulb's not being defective, when raised to the 1000th power, is 0.9<BR>\n" );
document.write( "x^1000=0.9<BR>\n" );
document.write( "log of both sides and 1000 log x=-0.04576 <BR>\n" );
document.write( "so log x=0.00004576<BR>\n" );
document.write( "raise x to the 10th power\r<BR>\n" );
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document.write( "x=0.99989 probably that a given bulb is not defective, so the probability one is defective is 0.0001054<BR>\n" );
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document.write( "Exactly 1 defective is<BR>\n" );
document.write( "probability exactly 1 is defective is 1000C1*0.99989^999*0.0001054=0.09443<BR>\n" );
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document.write( "At most 1 defective is 1- the above probability or 0.90557 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );