An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 1.2% of nonconforming items.
a) What is the probability that an item selected for inspection is classified as defective?
b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?
2007-11-20 15:55:16 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
D = Item is defective
G = Item is not defective (Good)
SD = Item is classified as defective
SG = Item is classified as not defective (Good)
P(D) = 0.012
P(G) = 0.988
P(SD|D) = P(SD∩D) / P(D) = 0.99
P(SG|D) = .01
P(SD|G) = 0.005
P(SG|G) = 0.995
(a) P(SD) = P(SD ∩ G) + P(SD ∩ D)
= P(SD|G) / P(G) + P(SD|D) / P(D)
=.005 * .988 + .99 * .012
=.01682
2007-11-20 16:15:21 · answer #1 · answered by Jeƒƒ Lebowski 6 · 4⤊ 0⤋
If 1.2% of items are defective, 98.8% are nondefective, so
a) 99% of the 1.2% defective are correctly identified, which is 1.188%, and 0.5% of the 98.8% nondefective are incorrectly identified as defective, which is 0.494%, for a total of 1.682% classified as defective.
b) 99.5% of the 98.8% nondefective are classified nondefective, 98.306%, and 1% of the 1.2% defective are also classified nondefective, 0.012%, for a total of 98.318%. Dividing by 98.8% actually nondefective, that's a probability of 99.512%.
2007-11-20 16:13:59 · answer #2 · answered by Philo 7 · 2⤊ 0⤋