Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps…

Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps has a defect probability of 1%. The final product produced on the assembly line is defective if any one of the 50 steps made a defect.

At the end of the assembly line there are two operators independently inspecting the product. Each of them is recognizing a defective product with a 90% probability. Assuming that the product is not defective, it is moved to the shipping department. Otherwise, the product is scrapped.

Probability that a defective product is produced (independent of the defect being found or not) (in decimal form):

What is the probability that a defective product is moved to the shipping department?

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