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A factory manufactures computers at two facilities, T₁ and T₂. Facility T₁ is responsible for 20% of the total production, while T₂ accounts for the remaining 80%. Overall, 7% of the computers produced are defective. It is given that the probability of a computer being defective when made at T₁ is ten times the probability of a computer being defective when made at T₂. If a randomly chosen computer from the factory is found to be non-defective, what is the probability that it was manufactured at T₂?
- 36/73
- 47/79
- 78/93
- 75/83
Correct answer: 78/93
Solution
Using Bayes' theorem, the probability of a non-defective computer being from T₂ is calculated. Given that T₁ produces 20% of computers with a defect rate 10 times that of T₂, the probability of a non-defective computer from T₂ is found to be 78/93.
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