Manufacturing process

Problem 1
Assume that 0.5% of all semiconductor parts produced in a manufacturing process break within one year. The parts can be tested with a very reliable but not perfect screening procedure:

2.5% of the parts that break within one year pass the test
1% of the parts that do not break within one year do not pass the test
A part just failed this test. What is the probability that this part will break within one year?

Sample Solution

30 miles southeast of the Big Easy sits Hopedale, built in between the winding channels of brackish water that serves as transportation systems for the guides and crabbers that inhabit this small town. I remember travelling to Hopedale for the first time in 6th grade and seeing the eye-opening conditions these blue-collar Louisiana natives live under. Hundreds of people lined the roads, fishing for redfish and speckled trout in the runoff trenches, not knowing that saltwater fish had no way of getting into these drainage systems, nonetheless living in them. Our group packed 12 people into two doublewide trailers, which proved to be a pain at 4:45 in the morning, with people scrambling around to find PFG shirts and Costa sunglasses before the Cajun guides left the docks. With lines in the water before daylight and fish striking lures faster than you could reel them in, we’d be worn out and ready to make the thirty-mile trek back to the docks around 3:00 in the afternoon.

Nicknamed “Sportsman’s Paradise”, the Mississippi River Delta earned its name due to the plethora of fresh and saltwater fish, oysters, shrimp, crabs, and millions of migrating waterfowl. The Mississippi River has deposited rich sediment in the warm waters of the Gulf of Mexico for thousands of years, allowing for the growth of plants, marshes, and barrier islands. This region stretches all the way across the southern coast of Louisiana, from the Vermilion Bay in southwest Louisiana to the Chandeleur Islands off the coast of Biloxi, Mississippi. The Delta is the largest drainage basin in the country, draining about 41% of the continental United States into the Gulf of Mexico.

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