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This is an incorrectly designed problem. The interviewer tries to ask the capability to handle conditional probability properly. This seemingly witty question can be resolved only when two events A: "Transistor is defective" B: "Test shows defective" are independent; In English, "test" is ineffective and it actually has no reliability to test the transistor's defectiveness. Otherwise, the probability of the intersection of two events cannot be expressed in the form of product of each event probability.
- Knoll October 11, 2013If the interviewer changed the question as follows, then the other people's suggested answers are correct.
"A bag contains many red or blue colored transistors. Among them 0.6% are defective. In every 100 non-defective transistors, two are red. You randomly pick one transistor and it turns out to be red. What is the probability that it is defective?"
Do you see the difference?