Manufacturing process

Problem 1
Assume that 0.5% of all semiconductor parts produced in a manufacturing process break within one year. The parts can be tested with a very reliable but not perfect screening procedure:

2.5% of the parts that break within one year pass the test
1% of the parts that do not break within one year do not pass the test
A part just failed this test. What is the probability that this part will break within one year?

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