We know the following regarding a colorimetric technique employed to test lake water for nitrates. If water specimens have nitrates, a solution dropped in the water will cause the specimen to turn red 95% of time. When employed on water specimens devoid of nitrates, the solution causes the water to turn red 10% of the time (since chemicals other than nitrates are sometimes present and they as well react to the agent). Past experiences in the lab point to that nitrates are contained in 30% of the water specimen that are sent to the lab for testing.
A. If a water specimen is randomly chosen from among those sent to the lab, what is the probability that it will turn red when tested?
B. If a water sample is randomly chosen and turns red when tested, compute the probability that it actually contains nitrates?