document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192369>Question 1192369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is common in many industrial areas to use<BR>\n" );
document.write( "a filling machine to fill boxes full of product. This<BR>\n" );
document.write( "occurs in the food industry as well as other areas in<BR>\n" );
document.write( "which the product is used in the home, for example,<BR>\n" );
document.write( "detergent. These machines are not perfect, and indeed<BR>\n" );
document.write( "they may A, fill to specification, B, underfill, and C,<BR>\n" );
document.write( "overfill. Generally, the practice of underfilling is that<BR>\n" );
document.write( "which one hopes to avoid. Let P(B)=0.001 while<BR>\n" );
document.write( "P(A)=0.990.<BR>\n" );
document.write( "(a) Give P(C).<BR>\n" );
document.write( "(b) What is the probability that the machine does not<BR>\n" );
document.write( "underfill?<BR>\n" );
document.write( "(c) What is the probability that the machine either<BR>\n" );
document.write( "overfills or underfills? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824265 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=824265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> as far as i know, the sum of all probabilities must be equal to 1.<BR>\n" );
document.write( "since there are only 3 possibilities, then the sum of those 3 probabilities must be equal to 1.<BR>\n" );
document.write( "p(a) = .990<BR>\n" );
document.write( "p(b) = .001<BR>\n" );
document.write( "(a) p(c) must be equal to 1 - .990 - .001 = 1 - .991 = .009.<BR>\n" );
document.write( "(b) the probability that the machine does not underfill is equal to 1 minus the probability that the machine does underfill = 1 minus p(b) = 1 minus .001 = .999, which is also equal to .990 (specs) plus .009 (overfill).<BR>\n" );
document.write( "(c) the probability that the machine either overfills or underfills is equal to 1 minus the probability that the machine fills to specifications = 1 minus .990 = .010, which is also equal to .001 (underfill) plus .009 (overfill).<BR>\n" );
document.write( "that's what i get.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );