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can someone help me solve this question? Thanks in advance!!Each week a retail outlet accepts delivery of a certain item from 3 different suppliers A, B and C. All the items received are put into an empty bin. A supplies 50% of these items, while B and C each supply 25%. From past experience, it is known that 2% of the items supplied by A are defective, 2% of the items supplied by B are defective and 4% of the items supplied by C are defective. Suppose an item is chosen at random from the bin. 4. [6] a) What is the probability that it is defective? b) What is the probability that this defective item came from supplier C?

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Answer #1

a)P(dfective)=P(from A and defective)+P(from B and defective)+P(from C and defective)

=0.5*0.02+0.25*0.02+0.25*0.04=0.025

b)P(from C|defective) =P(from C and defective)/P(defective)=0.25*0.04/0.025=0.4

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