document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104764>Question 1104764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability that a certain production process will produce a defective part is 0.20. If a box contains 12 parts, the probability that there will be 6 or 7 defective parts is ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719475 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=719475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a binomial probability type problem.\r<BR>\n" );
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document.write( "the probability that the process will produce a defective part is .2.\r<BR>\n" );
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document.write( "this makes p = .2\r<BR>\n" );
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document.write( "q is the probability that the process will not produce a defective part.\r<BR>\n" );
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document.write( "the probability of that is equal to 1 - .2 = .8\r<BR>\n" );
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document.write( "this makes q = .8\r<BR>\n" );
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document.write( "the formula for binomial probability is p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "c(n,x) is equal to n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "it's the number of ways you can get sets of x out of a set of n when the order of the elements within the set is not important.\r<BR>\n" );
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document.write( "so, your formula is p(x) = p^x * q^(n-x) = c(n,x).\r<BR>\n" );
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document.write( "n is equal to 12.\r<BR>\n" );
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document.write( "when x is equal to 6, the formula becomes p(6) = (.2)^2 * (.8)^6 * c(12,6).\r<BR>\n" );
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document.write( "when x is equal to 7, the formula becomes p(7) = (.2)^7 * (.8)^5 * c(12,7).\r<BR>\n" );
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document.write( "evaluate these equations and you get:\r<BR>\n" );
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document.write( "p(6) = .0155021476\r<BR>\n" );
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document.write( "p(7) = .0033218888\r<BR>\n" );
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document.write( "add them together and the probability of getting 6 or 7 defective parts is equal to .0188240364.\r<BR>\n" );
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document.write( "your solution is that the probability of getting 6 or 7 defective parts out of a batch of 12 parts is equal to .0188240364.\r<BR>\n" );
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document.write( "the following excel spreadsheet printout shows all the probabilities and confirms that the sum of all the probabilities must be equal to 1 and also confirms that the answer is correct.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src= \"http://theo.x10hosting.com/2017/121404.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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