A new disease has infected 0.02% of the population of a remote island. A test for diagnosing the disease has been developed such that the test is positive 95% of the times if the person has the disease and is negative 95% of the times if the person does not have the disease. The disease is especially prevalent among smokers with 3% of the smokers already infected. 0.2% people on the island smoke. It is important to note that the probability of an infected person testing positive is independent of whether or not that person is a smoker. Similarly, the probability of a noninfected person testing negative is independent of whether or not that person is a smoker. a. For a randomly chosen person from the island, if the test is positive, what is the probability that the person has the disease? E: First dene all relevant events carefully. b. A randomly chosen smoker tested positive with this test. What is the probability that this person has the disease? E: To solve this part, redefine the sample space to include only the smokers. c. If a person is known to have the disease, what is the probability that hefshe smokes