Probability of not detecting the impurity, Basic Statistics

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Probability of not detecting the impurity

A chemical engineer is interested in determining whether a 1 certain trace impurity is present in a product. An experiment has a probability of .80 of detecting the impurity if it is present.

The probability of not detecting the impurity if it is absent is .90. The prior probabilities of the impurity being present and being absent are .40 and .60, respectively. Three separate experiments result in only two detections. What is the posterior probability that the impurity is present?

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