A company produces lightbulbs at three factories A, B, and C. Factory A produces

Question

A company produces lightbulbs at three factories A, B, and C. Factory A produces 40% of the number of bulbs, of which 2% are defective. Factory B produces 35% of the number of bulbs, of which 4% are defective. Factory C produces 25% of the number of bulbs, of which 3% are defective. A defective bulb is found among the total output. Find the probability that it was produced in each of the three companies. Suppose a factory is chosen at random, and one of its bulb is randomly selected. If the bulb is defective, find the probability that it came from each one of the factories.

Explanation / Answer

The two questions seem to be asking for the same thing, but here isthe logic behind the possibility of a defect in each of thefactories: For each of the factories, you multiply the probability that thebulb came from that individual factory (i.e. .4 for A, .35 for B,.25 for C) by the probability of it being defective for thatspecific factory (for A, this would be .02). The resulting probability of a bulb being produced and defective inFactory A is (.4)*(.02)=0.008 or .8%

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