2) An x-ray system is used to detect flaws in the welds made at a turbine manufa

Question

2) An x-ray system is used to detect flaws in the welds made at a turbine manufacturing plant. The system is not perfect and sometimes misses flawed welds or identifies good welds as being flawed. A detailed study in which all welds were fully tested revealed that 2% of the welds identified as being good by the x-ray system were actually flawed and 80% of those identified as being flawed were actually flawed. Overall, the x-ray system identified 8% of the welds as being flawed. a) What is the probability that a randomly selected weld is flawed? b) If a weld is flawed, what is the probability that the x-ray system will identify it as flawed? c) If a weld is not flawed, what is the probability that the x-ray system will identify it as flawed?

Explanation / Answer

P(G|F) = 0.02 and P(G|F') = 0.98
P(G'|F) = 0.8 and P(G'|F') = 0.2
P(F) = 0.08 and P(F') = 0.92

a)
Required probability, P(F) = 0.08

b)
Required probabiltiy, P(G'|F) = 0.8

c)
Required probability, P(G'|F') = 0.2

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