After a component is manufactured, an automatic testing machine will process it,

Question

After a component is manufactured, an automatic testing machine will process it, and then declare it is either Good or Bad.
Unfortunately every time it tests a component, the automatic testing machine is wrong with probability 0.1.
For this reason, each component is tested 4 times ( one intial test and three re-tests).
If the automatic testing machine declares the part to be Bad for three or more of these tests, the component is thrown away.

A. Produce a formula for the probability that a component that is really good will be thrown away. Assume that the tests are independent.
B. Produce a formula for the probability that a component that is really bad will not be thrown away. Assume the tests are independent.

Explanation / Answer

A. Produce a formula for the probability that a component that is really good will be thrown away. Assume that the tests are independent. Type-1 error probability=0.01 B. Produce a formula for the probability that a component that is really bad will not be thrown away. Assume the tests are independent Type -2 error probability that is 0.05

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