document.write( "Question 1168486: Factories A, B and C produce computers. Factory A produces 3 times as many computers as factory C, and factory B produces 5 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.033, the probability that a computer produced by factory B is defective is 0.03, and the probability that a computer produced by factory C is defective is 0.035.\r
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Algebra.Com's Answer #793101 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Factories A, B and C produce computers. Factory A produces 3 times as many computers as factory C,
\n" ); document.write( "and factory B produces 5 times as many computers as factory C. The probability that a computer produced by factory A
\n" ); document.write( "is defective is 0.033, the probability that a computer produced by factory B is defective is 0.03,
\n" ); document.write( "and the probability that a computer produced by factory C is defective is 0.035.
\n" ); document.write( "A computer is selected at random and it is found to be defective. What is the probability it came from factory A?
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document.write( "Let x = # of computers produced by factory C.\r\n" );
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document.write( "Then factory A produces 3x computers, while factory B produces 5x computers.\r\n" );
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document.write( "In total, the amount of all produced computers is  Total = x + 3x + 5x = 9x.\r\n" );
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document.write( "The amount of defective computers produced by A is 0.033(3x);  by factory B is 0.03*(5x), and by factory C is 0.035x.\r\n" );
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document.write( "The total amount of defective computers produced by A, B and C together is  Total_defective = 0.033*(3x) + 0.03(5x) + 0.035x.\r\n" );
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document.write( "The problem's question is about the CONDITIONAL probability  P(comp is from A | comp is defective).\r\n" );
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document.write( "By the definition of the conditional probability,\r\n" );
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document.write( "    P(comp is from A | comp is defective) = .     (!)\r\n" );
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document.write( "The probability that the computer if from A and is defective is   =  = 0.011.\r\n" );
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document.write( "The probability that the computer is defective is  \r\n" );
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document.write( "     =  =  = 0.031556.\r\n" );
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document.write( "THEREFORE, the conditional probability (1) under the problem's question is\r\n" );
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document.write( "    P(comp is from A | comp is defective) =  =  = 0.348587.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "I presented the solution for you in the most detailed way.\r
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\n" ); document.write( "\n" ); document.write( "When a person gains some experience, he (or she) can do such calculations in a couple of lines.\r
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