A factory provides some items. The price is good, but 10 % of the items are defe

Question

A factory provides some items. The price is good, but 10 % of the items are defective. To eliminate some defective items, the factory introduces a new test. This test considers as good 99 % of the items that are good and consider as bad 98 % of the bad items. What is the probability that a bad item is considered as good by test? What is the probability that an item chosen at random is considered as good by the test? What is the probability that an item that has been considered as good by the test, is in fact a defective item? What advice should we give the factory manager?

Explanation / Answer

probabilty ofdefective =P(D)= 0.1

and good =P(G)=1-0.1=0.9

probabilty that test said good when given it is good =P(TG|G) =0.99

and probabilty that test said bad when given it is bad =P(TD|D) =0.98

1) probability that a bad item is considerd good =P(TG|D) =1-P(TD|D) =1-0.98=0.02

2)P(TG) =P(G)*P(TG|G)+P(D)*P(TG|D) =0.9*0.99+0.1*0.02=0.893

3)P(D|TG) =P(D)*P(TG|D)/P(TG) =0.1*0.02/0.893=0.00224

4)the factory manager needs to be advised to improve specificity of process., means claiming a bad unit to be bad by test,

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