XYZ, Inc. manufactures the same product in two of their plants, a Northern facil
ID: 3300035 • Letter: X
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.
Can you use formulas please like assigning A and P(A), P(A^c)....etc
Explanation / Answer
here let probabilty of being manufactured in Northern facility =P(N)=0.6 and that in Southern facility =P(S)=0.40
also probability of being returned =P(R) =0.08
probability that a customer returns his/her purchased product given that it was manufactured in the Southern facility
=P(R|S) =0.15
therefore P(RnS) =P(S)*P(R|S) =0.40*0.15=0.06
therefore probability that a product has been manufactured in the Southern facility if it has been returned to XYZ
=P(S|R) =P(RnS)/P(R) =0.06/0.08=0.75
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