Quality tester

Imagine that you are a quality manager on a production line assembling electrical appliances. Printed circuits are mounted into the appliances, and the functionality of the product depends on their flawlessness. The line is equipped with a tester - a control device that with a probability of 0.999 detects and discards a defective circuit. At the same time, the tester with a probability of 0.001 also discards from further processing a circuit without a defect. We further know that in the deliveries 0.1% of circuits are defective. What is the probability that a circuit that has passed through the tester has a defect? What is the probability that a circuit discarded from production has a defect?

Final Answer:

p₁ =  0.001
p₂ =  0.999

Step-by-step explanation:

$$\begin{gathered} p_0=0.1\%=\frac{0.1}{100}=0.001 \\ {p}_1=0.001\cdot (1-p_0)=0.001\cdot (1-0.001)=0.001 \end{gathered}$$

$p_2=1-p_1=1-0.001=0.999$

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