At a factory which produces hard drives, defective hard drives are produced according to a Poisson distribution at a rate of 12 per day. The company also hires inspectors to test for faulty hard drives. Of the defective hard drives, the inspectors are able to independently catch 90% of them. What is the probability that there 14 defective hard drives produced in a day? Given that there were 14 hard drives produced in a day, what is the probability that the inspectors identify 10 of them?

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