122 Section 7.6: Problem 7 (8 points) Factories A and B produce computers. Factory A produces 4 times as many computers as factory B. The probability that an item produced by factory A is defective is 0.021 and the probability that an item produced by factory B is defective is 0.037 . A computer is selected at random. What is the probability it came from factory A given it is found to be defective? Answer: (Hint: Draw a tree diagram.) Hint:Draw aree diagram. Answer: Previous Problem defective is 0.021 and the probability that an item produced by factory B is defective is 0.037. Problem List Next Problem 122 Section 7.6: Problem 7 A computer is selected at random. What is the probability it came from factory A given it is found to be defective?
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The overall probability of selecting a defective computer can be calculated by considering the probabilities of selecting a defective computer from factory A and factory B, weighted by the proportion of computers produced by each factory. Let x be the proportion Show more…
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A computer producing factory has only two plants $\mathrm{T}_{1}$ and $\mathrm{T}_{2} .$ Plant $\mathrm{T}_{1}$ produces $20 \%$ and plant $\mathrm{T}_{2}$ produces $80 \%$ of the total computers produced. $7 \%$ of computers produced in the factory turn out to be defective. It is known that $\mathrm{P}$ (computer turns out to be defective given that it is produced in plant $\mathrm{T}_{1}$ ) $=10 \mathrm{P}$ (computer turns out to be defective given that it is produced in plant $\mathrm{T}_{2}$ ), where $\mathrm{P}(\mathrm{E})$ denotes the probability of an event $\mathrm{E}$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $\mathrm{T}_{2}$ is [Adv. 2016] (a) $\frac{36}{73}$ (b) $\frac{47}{79}$ (c) $\frac{78}{93}$ (d) $\frac{75}{83}$
Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.033, the probability that a computer produced by factory B is defective is 0.045, and the probability that a computer produced by factory C is defective is 0.038. A computer is selected at random and it is found to be defective. What is the probability it came from factory B? Answer:
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Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 6 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.023, the probability that a computer produced by factory B is defective is 0.043, and the probability that a computer produced by factory C is defective is 0.052. A computer is selected at random and it is found to be defective. What is the probability it came from factory A?
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