document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916981>Question 916981</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Six items are taken at random from a box of 17 items and inspected. The box is rejected if more than 4 items are found to be faulty. If there are 6 faulty items in the box, find the probability that the box is rejected.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556450 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a binomial probability.<BR>\n" );
document.write( "the formula is:<BR>\n" );
document.write( "p(x) = c(n,x) * p^x * q^(n-x)\r<BR>\n" );
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document.write( "x is the number of defectives items.<BR>\n" );
document.write( "n is the total number of items.<BR>\n" );
document.write( "p is the probability of getting one that is defective.<BR>\n" );
document.write( "q is the probability of getting one that is not defective<BR>\n" );
document.write( "the probability of getting one that is not defective is equal to 1 minus the probability of getting one that is defective.\r<BR>\n" );
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document.write( "in this problem:<BR>\n" );
document.write( "n = 17<BR>\n" );
document.write( "x = 0 to 6<BR>\n" );
document.write( "p = 6/17 = .352941...<BR>\n" );
document.write( "q = 11/17 = .647058...\r<BR>\n" );
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document.write( "c(n,x) is the combination of n things taken x at a time where order doesn't matter.\r<BR>\n" );
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document.write( "this formula is:<BR>\n" );
document.write( "c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "you want to find the probability that more than 4 are defective out of 6 selected.\r<BR>\n" );
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document.write( "this means the probability that 5 or 6 are defective.\r<BR>\n" );
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document.write( "4 defective passes the test and the box is no rejected.<BR>\n" );
document.write( "5 or 6 defective fails the test and the box is rejected.\r<BR>\n" );
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document.write( "p(5) = c(6,5) * p^5 * q^1 = 6 * (6/17)^5 * (11/17)^1 = .021262...<BR>\n" );
document.write( "p(6) = c(6,6) * p^6 * q^0 = 1 * (6/17)^6 * (11/17)^0 = .001932...\r<BR>\n" );
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document.write( "add these together and you get p(5 or 6) = .023195 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "the probability that the box will be rejected = .023195 *****\r<BR>\n" );
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document.write( "the following excel spreadsheet shows all the probabilities.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/102601.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see that the total probability is equal to 1.<BR>\n" );
document.write( "you can slso see that the probability of 5 or 6 defectives when you pick 6 out of the box of 17 is equal to .023195.<BR>\n" );
document.write( "the column marked x contains the number of defectivdes.<BR>\n" );
document.write( "the column markes p(x) contains the probability of getting that many defectives.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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