Question

A production process produces an item, On average, 13% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 12% of the time. What proportion of the items will be "classified as good"?
I don't even need an answer, just an explanation would be great

Answer 1

out of a thousand items:
130 are broken , 870 are ok

out of the 130 broken, 15.6 are mistakenly labeled good
out of the 870 good, 20.4 are mistakenly labeled broken, so 849.6 classified good
so
15.6 + 849.6 = 865.2 are labeled good
100 * (865.2/1000) = 86.5 % are classified "good"
(although in fact 15.6 or 100(15.6/849.6)= 1.8% of those are actually broken and mistakenly labeled good)