We know the following about a colorimetric method used to test lake water for nitrates. If water specimens contain nitrates, a solution dropped into water will cause the specimen to turn red 90% of the time. When used on water specimen without nitrates, the solution causes the water to turn red 15% of the time (because chemicals other than nitrates might also be present and react to the agent). Past experience in a lab indicates that nitrates are contained in 15% of the water specimens that are sent to the lab for testing.

(a) If a water specimen is randomly selected from among those sent to the lab, what is the probability that it will turn red when tested? (3.d.p)

(b) If a water specimen is randomly chosen and turns red when tested, what is the probability that it actually contains the nitrates? (3.d.p)