document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183756>Question 1183756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The quality assurance engineer of a receiving-sets manufacturer inspects receiving-sets in lots of 50. He selects 5 of the 50 receiving-sets at random and inspects them thoroughly. Assuming that 6 of the 50 receiving-sets in the current lot are defective, find the probability that exactly 2 of the 5 receiving-sets selected by the engineer are defective. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814245 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=814245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability of a set being defective is 6/50 = .12.<BR>\n" );
document.write( "the probability of a wet not being defective is 1 - .12 = .88\r<BR>\n" );
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document.write( "you select 5 of the 50 at random.\r<BR>\n" );
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document.write( "the formula to use is p(x) = p^x * q^(n-x) * c(n,x).<BR>\n" );
document.write( "p is the probability of the set being defective.<BR>\n" );
document.write( "q is the probability of the set not being defective.<BR>\n" );
document.write( "n is equal to 5.<BR>\n" );
document.write( "x is equal to 0 to 5.<BR>\n" );
document.write( "c(n,x) is equal to n! / (x! * (n-x)!).\r<BR>\n" );
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document.write( "you want the probability that exactly 2 of the 5 sets selected at random are defective.\r<BR>\n" );
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document.write( "p(2) = .12^2 * .88^(5-2) * c(5,2) = .12^2 * .88^3 * c(5,2) = .12^2 * .88^3 * 10 = .098131968.\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "all the probabilities are shown below:\r<BR>\n" );
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document.write( "the eum of all probabilities is equal to 1, as it should be.\r<BR>\n" );
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document.write( "probability of exactly 2 defective sets is p(2) = .098131968, which is equal to .098132 when rounded to 6 decimal digits.<BR>\n" );
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