Say you’re a chemical engineer studying whether a certain trace impurity is present in a product. An experiment has a probability of 0.80 of detecting the impurity if it is present. The probability of not detecting the impurity if it is absent is 0.90. You have reason to believe that 40% of products actually contain the impurity. You perform an experiment which detected an impurity – what is the probability that the impurity is not really there?

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