A smart phone manufacturer has two factories (A and B). Factory A produces 40% of the smart phones and factory B produces the remaining 60%. Factory A has a defect rate of 1/80 while factory B has a defect rate of 1/60. When we find a defective smart phone, what is the probability that it is from factory A?  We have found two defective smart phones. If one of them is from factory A, what is the probability that both of the phones are from factory A?  We have found two defective smart phones. If at least one of them is from factory A, what is the probability that both of the phones are from factory A?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A smart phone manufacturer has two factories (A and B). Factory A produces 40% of the smart phones and factory B produces the remaining 60%. Factory A has a defect rate of 1/80 while factory B has a defect rate of 1/60.

  1. When we find a defective smart phone, what is the probability that it is from factory A? 
  2. We have found two defective smart phones. If one of them is from factory A, what is the probability that both of the phones are from factory A? 
  3. We have found two defective smart phones. If at least one of them is from factory A, what is the probability that both of the phones are from factory A?
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