document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163204>Question 1163204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.Consider a production of 450 parts, 50 parts of them do not conform to customer requirements, four parts are selected randomly. What is the probability that at least two of them do not conform to customer requirements.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787226 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=787226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Probability of a bad part for any random selection: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{50}{450}\ =\ \frac{1}{9}\">\r<BR>\n" );
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document.write( "Probability of at least two successes out of four trials with a probability of success = <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{9}\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P\(\geq\,2,4,\frac{1}{9}\)\ =\ \sum_{r=2}^4\,\ {{4}\choose{r}}\,(\frac{1}{9}\)^r\,\cdot\,\(\frac{8}{9}\)^{4-r}\">\r<BR>\n" );
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document.write( "However, the following is equivalent and less arithmetic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P\(\geq\,2,4,\frac{1}{9}\)\ =\ 1\ -\ P\(\leq\,1,4,\frac{1}{9}\)\ =\ 1\ -\ \sum_{r=0}^1\,{{4}\choose{r}}\,(\frac{1}{9}\)^r\,\cdot\,\(\frac{8}{9}\)^{4-r}\">\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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