Question

A production line has an automatic scanner to detect defects. In recent production, 10% of items have been defective. Every defective item is identified correctly as defective with probability 90%. Every non-defective item is identified correctly as non-defective with probability 80%.

Required:
What percent of all the items are classified correctly by the scanner?

Answer 1

81%

Explanation:

P (Defective item) = 10% , P (Defective identified) = 90% of defective = 90% of 10% = 9%

P (Non defective item) = 1 - 10% = 90% , P (Non defective identified) = 80% of non defective = 80% of 90% = 72%

Prob (Scanner identifies correctly) = Pr (non defective mentioned non defective) & Pr (defective mentioned defective)

= 9% + 72% = 81%