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Probability - Random Variables

An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a .5% chance of incorrectly classifying a good item asdefective. The company has evidence that its line produces .9% 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 non-defective, what is the probability that it is indeed good?
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Answer #1
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(SDnD) / P(D) = 0.99
P(SG|D) = .01
P(SD|G) = 0.005
P(SG|G) = 0.995
answered by: arcanejak
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Answer #2
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(SDnD) / P(D) = 0.99
P(SG|D) = .01
P(SD|G) = 0.005
P(SG|G) = 0.995



(a) P(SD) = P(SD n G) + P(SD n D)
= P(SD|G) / P(G) + P(SD|D) / P(D)
=.005 * .988 + .99 * .012
=.01682
answered by: lora
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