SOLUTION: 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 blad

Algebra ->  Probability-and-statistics -> SOLUTION: 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 blad      Log On


   

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
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
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Let me re-write the condition in a correct way, as it should be: 

    In a razor blade factory, machines A,B and C manufacture 25%, 35% and 40% of the total output respectively. 
    Of their respective outputs, 5%, 4% and 2% are defective razor blades. A razor blade is chosen at random and found to be defective. 
    Find the probability that it was manufactured by machine B


Solution 

Let X = the total output amount of razor blades produced by all three machines A, B and C.


Then the machine A produces  0.25*X blade razors;   of them, 0.05*0.25*X razors are defective.

     The machine B produces  0.35*X blade razors;   of them, 0.04*0.35*X razors are defective.

     The machine C produces  0.40*X blade razors;   of them, 0.02*0.40*X razors are defective.


The probability under the question is the ratio of the defective razors amount produced by the machine B, 0.04*0.35*X, 
to the total amount of all defective razors produced by all 3 machines.


In other words, the probability under the question is this ratio


    P = %280.04%2A0.35%2AX%29%2F%280.05%2A0.25%2AX+%2B+0.04%2A0.35%2AX+%2B+0.02%2A0.40%2AX%29 = %280.04%2A0.35%29%2F%280.05%2A0.25+%2B+0.04%2A0.35+%2B+0.02%2A0.40%29 = 0.4058 = 40.58% (approximately).

Solved.