A manufacturing firm purchases a certain component, for its manufacturing process, from three sub-contractors A, B and C. These supply 60%, 30% and 10% of the firm's requirements, respectively. It is known that 2%, 5% and 8% of the items supplied by the respective suppliers are defective. On a particular day, a normal shipment arrives from each of the three suppliers and the contents get mixed. A component is chosen at random from the day's shipment : (a) What is the probability that it is defective? (b) If this component is found to be defective, what is the probability that it was supplied by (i) A, (ii) B, (iii) C?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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A manufacturing firm purchases a certain component, for its
manufacturing process, from three sub-contractors A, B and C.
These supply 60%, 30% and 10% of the firm's requirements,
respectively. It is known that 2%, 5% and 8% of the items supplied
by the respective suppliers are defective. On a particular day, a
normal shipment arrives from each of the three suppliers and the
contents get mixed. A component is chosen at random from the
day's shipment :
(a) What is the probability that it is defective?
(b) If this component is found to be defective, what is the
probability that it was supplied by (i) A, (ii) B, (iii) C?
Transcribed Image Text:A manufacturing firm purchases a certain component, for its manufacturing process, from three sub-contractors A, B and C. These supply 60%, 30% and 10% of the firm's requirements, respectively. It is known that 2%, 5% and 8% of the items supplied by the respective suppliers are defective. On a particular day, a normal shipment arrives from each of the three suppliers and the contents get mixed. A component is chosen at random from the day's shipment : (a) What is the probability that it is defective? (b) If this component is found to be defective, what is the probability that it was supplied by (i) A, (ii) B, (iii) C?
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