XYZ, Inc. manufactures the same product in two of their plants, a Northern facil

Question

XYZ, Inc. manufactures the same product in two of their plants, a Northern facility and a Southern facility. Customers who purchase from XYZ, Inc. are encouraged to return their products if they are defective. The probability that a customer returns his/her purchased product given that it was manufactured in the Southern facility is 0.15. The Southern facility produces 40% of the products. It has been recorded that 8% of the customers return their product. What is the probability that a product has been manufactured in the Southern facility if it has been returned to XYZ, Inc.

Explanation / Answer

Ans:

Given that

P(return product/southern facility)=0.15

P(return product)=0.08

P(southern facility)=0.4

Now,calculate:

P(southern facility/return product)=P(return product/southern facility)*P(southern facility)/P(return product)

=(0.15*0.4)/0.08

=0.06/0.08

=3/4

=0.75

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