Question 1205005
A production process produces an
item. On average, 15% of all items produced are
defective. Each item is inspected before being shipped,
and the inspector misclassifies an item 10% of the time.
What proportion of the items will be “classified as
good”?<pre> 
P[(good AND cl. good) OR (def. and cl. good)] =(0.85)(0.90) + (0.15)(0.10) = 0.78</pre>
What is the probability that an item is defective given that it was classified
as good?<pre>
P(def.|cl. good) = P(def. AND cl. good)/P(cl. good)

P(def. AND cl. good) = (0.15)(0.10) = 0.015

P(cl. good) = 0.78 

P(def|cl. good) = P(def AND cl. good)/P(cl. good) = 0.015/0.78 = 15/780 = 1/52

Edwin</pre>