Question

A quality control department finds that it accepted only 5% of all bad items and it rejected only 1% of good items. A supplier has just delivered a shipment of a certain item. Past records show that only 90% of the parts of that supplier are good. If the department accepts an item, what is the probability that the item is bad? Round your answer to five decimal places.

A. 0.05000  

B. None of the choices are correct  

C. 0.09635

D. 0.00558

  

Answer 1

Solution:

A quality control department finds that it accepted only 5% of all bad items and it rejected only 1% of good items. A supplier has just delivered a shipment of a certain item. Past records show that only 90% of the parts of that supplier are good. If the department accepts an item, what is the probability that the item is bad

Let A, R denote that the item is acccepted or rejected respectively.

Let B,G denote that the item is bad or good respectively.

Given , P(A|B) = 0.05 P(R|B)= 1-0.05 = 0.95

P(G)=0.90 P(B) = 1- 0.90 = 0.10

P(R|G)= 0.01    P(A|G) = 1-0.01 = 0.99

so,   

Hence the correct option is (D) 0.0058

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Thank you.