Suppose it is known that 1 part in 1000 produced by an aircraft supplier is bad. each part can be screened for defects using x-rays. if the part is bad, the x-ray test will detect it with probability 0.999. if the part is good, there is a probability of 0.002 that it is erroneously indicated as bad by the x-ray test. for one randomly selected part, the test shows that it is bad. what is the probability that it is really bad (hint: this is a conditional probability)?