document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189786>Question 189786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. What is the probability that out of six keyboards selected at random, exactly zero keyboards will be defective? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142391 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "If there is a 5% probability that a keyboard will be defective, then there is a 95% probability that it will have no defects.  So for a sample of six keyboards, whether or not any of them are defective is six independent events -- meaning that whether the first one is defective has no effect on whether any of the others are defective, and so on.\r<BR>\n" );
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document.write( "Hence, the probability that none of them will be defective is the product of the probabilities that each of them individually is not defective:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  .95 \times .95 \times .95 \times .95 \times .95 \times .95 = .95^6 \approx .735\">\r<BR>\n" );
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document.write( "or 73.5%\r<BR>\n" );
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document.write( "Windows calculator: .95, \"x^y\" button, 6, \"=\" button.\r<BR>\n" );
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document.write( "Looking at it another way, the odds are better than 1 in 4 that one of the six <i><b>will</b></i> be defective.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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