document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202709>Question 1202709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is common in many industrial areas to use a filling machine to fill boxes full of products. This occurs in the food<BR>\n" );
document.write( "industry as well as other areas in which the product is used in the home, for example, detergent. These machines<BR>\n" );
document.write( "are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally, the practice<BR>\n" );
document.write( "of underfilling is that which one hopes to avoid. Let P(B) = 0.001 while P(A) = 0.990.<BR>\n" );
document.write( "i. Give P(C).<BR>\n" );
document.write( "ii. What is the probability that the machine does not underfill?<BR>\n" );
document.write( "iii. What is the probability that the machine either 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 #837773 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52874)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "It is common in many industrial areas to use a filling machine to fill boxes full of products. <BR>\n" );
document.write( "This occurs in the food industry as well as other areas in which the product is used in the home, <BR>\n" );
document.write( "for example, detergent. These machines are not perfect, and indeed they may <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;A, &nbsp;&nbsp;fill to specification, <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;B, &nbsp;&nbsp;underfill, and <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;C, &nbsp;&nbsp;&nbsp;overfill. <BR>\n" );
document.write( "Generally, the practice of underfilling is that which one hopes to avoid. <BR>\n" );
document.write( "Let P(B) = 0.001 while P(A) = 0.990.<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;Give P(C).<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;&nbsp;What is the probability that the machine does not underfill?<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;(c) &nbsp;&nbsp;What is the probability that the machine either overfills or underfills?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Obviously, the introduced terms describe disjoint events, \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;that have zero intersections in the probability theory meaning.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, the probabilities of combinations of events are the sums of elementary events.\r<BR>\n" );
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document.write( "(a)  P(A) + P(B) + P(C) = 1.  \r\n" );
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document.write( "     THEREFORE,  P(C) = 1 - P(A) - P(B) = 1 - 0.990 - 0.001 = 0.009.    <U>ANSWER</U>\r\n" );
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document.write( "(b)  P(does not underfill) = P(not B) = 1 - P(B) = 1 - 0.001 = 0.999.   <U>ANSWER</U>\r\n" );
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document.write( "(c)  P(either overfills or underfills) = P(C) + P(B).\r\n" );
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document.write( "     Again, notice that we just know P(C) = 0.009 from (a).\r\n" );
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document.write( "     THEREFORE,  P(either overfills or underfills) = P(C) + P(B) = 0.009 + 0.001 = 0.01.    <U>ANSWER</U>\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "It is very easy problem, and its major goal is to check if the student is able to read the problem,<BR>\n" );
document.write( "to understand the basic terms and their inter-relations, and to check<BR>\n" );
document.write( "if he (or she) knows basic relations/formulas of the elementary probability theory.\r<BR>\n" );
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document.write( "I specially re-formatted the text in your post for easy reading.\r<BR>\n" );
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document.write( "This problem is good for those who make their first steps in learning the probability theory.\r<BR>\n" );
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document.write( "For all other persons, the solution is more than evident.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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