There are two suppliers for an operation. Supplier A supplies 80% of the raw mat

Question

There are two suppliers for an operation. Supplier A supplies 80% of the raw material, supplier B 20%. Supplier A has a defect rate of 2% and supplier B has a scrap rate of 8%. Given the raw material is found defective, what is probability that it came from supplier A?

There are two suppliers for an operation. Supplier A supplies 80% of the raw material, supplier B 20%. Supplier A has a defect rate of 2% and supplier B has a scrap rate of 8%. Given the raw material is found defective, what is probability that it came from supplier A?

Explanation / Answer

P(A) = 0.80, P(B) = 0.20

P(Defective | A) = 0.02, P(Defective | B) = 0.08

P( A | Defective) = ?

Using Bayes' conditional probability theorem.

P( A | Defective) = P(A) * P( Defective | A ) / { P(A) * P( Defective | A ) + P(B) * P( Defective | B ) }

= 0.8 * 0.02 / { 0.8 * 0.02 + 0.20 * 0.08 }

= 0.50

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