An inspector working for a manufacturing company has a 95 ch

An inspector working for a manufacturing company has a 95% chance of correctly identifying defective items and 2% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 1% of defective items. What is the probability that an item selected for inspection is classified as defective? If an item selected at random is classified as nondefective, what is the probability that it is indeed good?

Solution

P(Good item) = 0.99

P(Defective) = 0.01

a)

If the item is classified as a defective piece, the probability is:

P(A) = P(Good item as defective) + P (Defective item as defective)

= 0.99 * 0.02 + 0.01*0.95

= 0.0293

b)

Given that item is identified as non-defective,

P (B) = P (Good item identified as good) + P(Defective item identified as good)

= (0.99 * 0.98) + (0.01*0.05)

= 0.9707

Probability that it is actually non-defective

= (0.99 * 0.98) / 0.9707

= 0.9994

Hope this helps.