document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997079>Question 997079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question is really confusing me, not quite sure where to start.\r<BR>\n" );
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document.write( "A foreman for an injection-molding firm admits that on 39% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 4% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?\r<BR>\n" );
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document.write( "Probability = ? </SPAN>\n" );
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document.write( "Given:<BR>\n" );
document.write( "A foreman forgets to shut off machine 39% of the time.<BR>\n" );
document.write( "If he forgets, 15% of moulds are defective.<BR>\n" );
document.write( "If he does not, 4% of moulds are defective.<BR>\n" );
document.write( "Given that a mould is defective, find probability that he forgot to turn off machine the night before.<BR>\n" );
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document.write( "Solution:<BR>\n" );
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document.write( "Define events<BR>\n" );
document.write( "1. F = event of forgetting to shut off machine.<BR>\n" );
document.write( "2. D = event of product being defective.\r<BR>\n" );
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document.write( "P(F and D) = 0.39*0.15=0.0585<BR>\n" );
document.write( "P(F and ~D) = 0.39*(1-0.15)=0.3315<BR>\n" );
document.write( "P(~F and D) = (1-0.39)*0.04=0.0244<BR>\n" );
document.write( "P(~F and ~D) = (1-0.39)*(1-0.04)=0.5856<BR>\n" );
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document.write( "By definition of conditional probability<BR>\n" );
document.write( "P(F|D)=P(F and D)/P(D)<BR>\n" );
document.write( "=P(F and D)/[P(F and D)+P(~F and D)]<BR>\n" );
document.write( "=0.0585/(0.0585+0.0244)<BR>\n" );
document.write( "=0.706 (approx.)<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "The probability that the foreman forgot to shut the machine is 0.706, given that the product was defective. </SPAN>\n" );
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