1. A doctor studies the known cancer patients in a certain town. The probability that a randomly chosen resident has cancer is found to be .001. It is found that 30% of the town works for Ajax Chemical Company. The probability that an employee of Ajax has cancer is equal to .003. Are the events "has cancer" and "works for Ajax" independent of one another?
2. A hospital uses two tests to classify blood. Every blood sample is subjected to both tests. The first test correctly identifies blood type with probability .7, and the second test correctly identifies blood type with probability .8. The probability that at least one of the tests correctly identifies the blood type is .9.
(a) Find the probability that the second test is correct, given that the first test is correct.
(b) Are the events "test I correctly identifies the blood type" and "test II correctly identifies the blood type" independent?