The use of plant appearance in prospecting for ore deposits is called geobotanical prospecting. One indicator of copper is a small mint with a mauve-colored flower. Suppose that, for a given region, there is a 30% chance that the soil has a high copper content and a 23% chance that the mint will be present there. If the copper content is high, there is a 70% chance that the mint will be present.
(a) Find the probability that the copper content will be high and the mint will be present.
(b) Find the probability that the copper content will be high given that the mint is present.
(c) Are the events A1: the mint is present, and A2: the soil has a high copper content independent?