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.
1- What is the probability that a unit ends up in rework (in decimal form)?
2- What is the probability that a defective unit is shipped (in decimal form)?

1. Probability that a unit ends up in rework = Probability of defect in 20 stations multiplied by the probability of catching defects = 0.8%(1% x 80%) = 0.008

2. Probability that a defective unit is shipped = Probability of defective units during inspection plus Probability of defective units during rework = 25% (20% + (100-95%)) = 0.25

Explanation:

a) Probability of defect in 20 stations = 0.5% x 20 = 1%.  Each station has a 0.05%

b) Probability of defective units during inspection = 20% (100% - 80)

c) Probability of defective units during rework = 5% (100% -95)

c) Probability is the likelihood or chance of an event occurring.  Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring.

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