20-Station Assembly Line

Consider an assembly line with 20 stations. Each station has a 0.5% probability of making a defect. At the end of the line, an inspection step singles out the defective units. The inspection step catches 80% of all defects. From inspection, units that are deemed to be non-defective are moved to the shipping department.

If a defect is found at inspection, it is sent to the rework department. Rework fixes about 95% of the defective units. Units are directly shipped from the rework department with no further inspection taking place.

What is the probability that a unit ends up in rework (in decimal form)?

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