document.write( "Question 1116516: In a razor balde factory, machines A,B abd C manufacture 25%, 35% and 40% of the total output respectively. of theri outputs, 5%, 4% and 2% are defective razor blades. A razor blade is chosen at random and found to be defective. a razor blade is selected at random and it is found to be defective. find the probability that it was manufactured by machine B \n" ); document.write( "

Algebra.Com's Answer #731414 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Let me re-write the condition in a correct way, as it should be:\r
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document.write( "    In a razor blade factory, machines A,B and C manufacture 25%, 35% and 40% of the total output respectively. \r\n" );
document.write( "    Of their respective outputs, 5%, 4% and 2% are defective razor blades. A razor blade is chosen at random and found to be defective. \r\n" );
document.write( "    Find the probability that it was manufactured by machine B\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution\r
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document.write( "Let X = the total output amount of razor blades produced by all three machines A, B and C.\r\n" );
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document.write( "Then the machine A produces  0.25*X blade razors;   of them, 0.05*0.25*X razors are defective.\r\n" );
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document.write( "     The machine B produces  0.35*X blade razors;   of them, 0.04*0.35*X razors are defective.\r\n" );
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document.write( "     The machine C produces  0.40*X blade razors;   of them, 0.02*0.40*X razors are defective.\r\n" );
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document.write( "The probability under the question is the ratio of the defective razors amount produced by the machine B, 0.04*0.35*X, \r\n" );
document.write( "to the total amount of all defective razors produced by all 3 machines.\r\n" );
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document.write( "In other words, the probability under the question is this ratio\r\n" );
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document.write( "    P =  =  = 0.4058 = 40.58% (approximately).\r\n" );
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