We know the following about a colormetric method used to test lake water for nitrates

Chapter 2, Problem 2.152

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We know the following about a colormetric method used to test lake water for nitrates. If water specimens contain nitrates, a solution dropped into the water will cause the specimen to turn red 95% of the time. When used on water specimens without nitrates, the solution causes the water to turn red 10% of the time (because chemicals other than nitrates are sometimes present and they also react to the agent). Past experience in a lab indicates that nitrates are contained in 30% of the water specimens that are sent to the lab for testing. If a water specimen is randomly selected a from among those sent to the lab, what is the probability that it will turn red when tested? b and turns red when tested, what is the probability that it actually contains nitrates?

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