Three companies supply light bulbs to a university. Company A provides the unive

ID: 3256471 • Letter: T

Question

Three companies supply light bulbs to a university.

Company A provides the university with 65% of its light bulbs, and have a 8% chance of failing within a year.

Company B provides the university with 15% of its light bulbs, and have a 6% chance of failing within a year.

Company C provides the university with 20% of its light bulbs, and have a 1% chance of failing within a year.

What is the probability that a particular defective light bulb originated from Company C?

14.2%

19.9%

82.6%

3.2%

Three companies supply light bulbs to a university.

Company A provides the university with 65% of its light bulbs, and have a 8% chance of failing within a year.

Company B provides the university with 15% of its light bulbs, and have a 6% chance of failing within a year.

Company C provides the university with 20% of its light bulbs, and have a 1% chance of failing within a year.

What is the probability that a particular defective light bulb originated from Company C?

Answers:

14.2%

19.9%

82.6%

3.2%

Lat A, B and C shows the events that bulbs are made by company A, B and C respectively. So

P(A) = 0.65, P(B) = 0.15, P(C) = 0.20

Let F shows the event that bulb is failing within a year. So

P(F|A) = 0.08, P(F|B) = 0.06, P(F|C) = 0.01

By the law of total probability, the probability that bulb is failing within a year is

P(F) = P(F|A)P(A)+ P(F|B)P(B)+ P(F|C)P(C) = 0.08 *0.65 + 0.06*0.15 + 0.01*0.20 = 0.052 + 0.009 + 0.002 = 0.063

Now the probability that a particular defective light bulb originated from Company C is

P(C|F) = [P(F|C)P(C) ] / P(F) = [0.01*0.20] / 0.063 = 0.032

That is answer is : 3.2%

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