Question

Two qualified inspectors are hired to inspect major vehicle components (transmission, engines, axle assemblies, and other large items). These employees will be the last personnel to look at any item before it is prepared for shipment. They are the last link in the manufacturing chain. One inspector (Mr. A) has been doing this type of work for nearly 15 years. The other person (Mr. B) is comparatively new, but still has developed a fine track record. He has been inspecting for two years. Nobody is perfect and occasionally a discrepancy or potential problem is missed. The likelihood that Mr. A performs a completely perfect inspection is .90. Mr. B has an 80% accuracy rate for inspecting. These inspectors operate independently in separate but similar areas in the pre-shipment zones of the company. However, each performs his own inspection on every item utilizing a two-man rule.

3. What is the likelihood that only one inspector performs a perfect inspection?

4. What is the chance that both inspectors missed discrepancies or problem areas that existed?

5. What is the chance that Mr. A missed a potential problem in his inspection given that Mr. B performed his perfectly?

Answer 1

Consider the image above for the numerical solution to the above question. The likelihood that only one inspector performs a perfect inspection is 0.26. The chance that both inspectors missed discrepancies or problem areas that existed is 0.02. The chance that Mr. A missed a potential problem in his inspection given that Mr. B performed his perfectly is 0.1.