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Three factories produce light bulbs to supply the market. Factory A produces 40%, 20% of the tools are produced in factory B and 40% in fact
Question
Three factories produce light bulbs to supply the market. Factory A produces 40%, 20% of the tools are produced in factory B and 40% in factory C. 5% of the bulbs produced in factory A, 3% of the bulbs produced in factory B and 4% of the bulbs produced in factory C are defective.A bulb is selected at random in the market and found to be defective. What is the probability that this bulb was produced by factory A?
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Mathematics
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2021-08-22T13:36:53+00:00
2021-08-22T13:36:53+00:00 1 Answers
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Answer:
0.4762 = 47.62% probability that this bulb was produced by factory A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
P(A) is the probability of A happening.
In this question:
Event A: Bulb is defective.
Event B: Produced by factory A.
Probability of a bulb being defective.
5% of 40%(factory A)
3% of 20%(factory B)
4% of 40%(factory C). So
Defective and from factory A:
5% of 40%. So
What is the probability that this bulb was produced by factory A?
0.4762 = 47.62% probability that this bulb was produced by factory A