document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034977>Question 1034977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shipment of 1313 microwave ovens contains 33 defective units. A restaurant buys four of these units. What is the probability of the restaurant buying at least three nondefective&#8203; units?<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 #649627 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "A shipment of 1313 microwave ovens contains 33 defective units. A restaurant buys four of these units. What is the probability of the restaurant buying at least three nondefective&#8203; units?<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "At least three non-defective is the same as three non-defective or four non-defective.<BR>\n" );
document.write( "Using the hypergeometric distribution:<BR>\n" );
document.write( "A=33,B=1313-33=1280<BR>\n" );
document.write( "C(n,r)=n!/(r!(n-r)!)<BR>\n" );
document.write( "Case one: 3 non-defectives<BR>\n" );
document.write( "a=1, b=3<BR>\n" );
document.write( "P(a,b)=C(A,a)*C(B,b)/C(A+B,a+b)<BR>\n" );
document.write( "=C(33,3)*C(1280,1)/C(1313,4)<BR>\n" );
document.write( "=287682912/3081777751<BR>\n" );
document.write( "Case two: 4 non-defectives<BR>\n" );
document.write( "a=0,b=4<BR>\n" );
document.write( "P(a,b)=C(A,a)*C(B,b)/C(A+B,a+b)<BR>\n" );
document.write( "=C(33,0)*C(1280,4)/C(1313,4)<BR>\n" );
document.write( "=2783114232/3081777751\r<BR>\n" );
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document.write( "Probability of at least three non-defectives<BR>\n" );
document.write( "=287682912/3081777751+2783114232/3081777751<BR>\n" );
document.write( "=3070797144/3081777751<BR>\n" );
document.write( "=0.99644 approximately\r<BR>\n" );
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document.write( "Note:<BR>\n" );
document.write( "since 33 is small compared to 1313, binomial distribution would give a close approximation.<BR>\n" );
document.write( "p=33/1313=0.025133<BR>\n" );
document.write( "P(3, or 4 non-defective)<BR>\n" );
document.write( "=C(4,1)*p^1*(1-p)^4+C(4,0)*p^0*(1-p)^4<BR>\n" );
document.write( "=0.093142+0.903193<BR>\n" );
document.write( "=0.99634\r<BR>\n" );
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