Strain gauges are assembled on production lines A , B , and C , and packaged in
ID: 3129816 • Letter: S
Question
Strain gauges are assembled on production lines A, B, and C, and packaged in batches of 10. Each day, the quality control team selects a production line by probability sampling with probabilities P(A)=P(B)=0.3, and P(C)=0.4. They then inspect a randomly drawn batch from the selected production line. The probability that no problems are found in a batch selected from production line A is 0.99, and the corresponding probabilities are 0.97 and 0.92 for production lines B and C, respectively.
a. Compute the probability a batch from production line A is inspected and no problems are found.
b. Compute the probability no problems are found on a given day.
c. Given no problems were found on a given day, what is the probability that the inspected batch came from production line C?
Explanation / Answer
a) 0.297
b) 0.956
c) 0.3849
Event Prior Probability Conditional Probability Joint Probability Revised Probability A 0.3 0.99 0.297 0.3107 B 0.3 0.97 0.291 0.3044 C 0.4 0.92 0.368 0.3849 0.956 1