1. The Ponderosa Paint and Glass Company (PP&G Co.) makes paint at three locatio
ID: 2932083 • Letter: 1
Question
1. The Ponderosa Paint and Glass Company (PP&G Co.) makes paint at three locations. Each location ships unmarked paint cans to a central warehouse for national distribution. Plant A supplies 50% of the paint, Plant B supplies 30% of the paint and Plant C supplies the remaining 20% of the paint. Past records indicate that Plant A incorrectly mixes paint 10% of the time, Plant B incorrectly mixes paint 5% of the time while Plant C incorrectly mixes paint 15% of the time. PP&G Co. guarantees its product and spent $20,000 replacing incorrectly mixed paint last year. If a paint can is incorrectly mixed, find the probability that it came from
a. Plant A.
b. Plant B.
c. Plant C.
Explanation / Answer
P(plant A) = 0.5
P(plant B) = 0.3
P(plant C) = 0.2
P(incorrectly mixed | plant A) = 0.1
P(incorrectly mixed | plant B) = 0.05
P(incorrectly mixed | plant C) = 0.15
P(incorrectly mixed) = P(incorrectly mixed | plant A) * P(plant A) + P(incorrectly mixed | plant B) * P(plant B) + P(incorrectly mixed | plant C) * P(plant C)
= 0.1 * 0.5 + 0.05 * 0.3 + 0.15 * 0.2
= 0.095
a) P(plant A | incorrectly mixed) = P(incorrectly mixed | plant A) * P(plant A) / P(incorrectly mixed)
= 0.1 * 0.5 / 0.095
= 0.5263
b) P(plant B | incorrectly mixed) = P(incorrectly mixed | plant B) * P(plant B) / P(incorrectly mixed)
= 0.05 * 0.3 / 0.095
= 0.1579
c) P(plant C | incorrectly mixed) = P(incorrectly mixed | plant C) * P(plant C) / P(incorrectly mixed)
= 0.15 * 0.2 / 0.095
= 0.3158
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