You are diagnosed with a rare disease. you know that there only is a 1% chance of getting it. use the letter d for the event "you have the disease" and t for "the test says so". it is known that the test is imperfect: p(t|d) = 0.98 and p(tc|dc) = 0.95. (a) given that you test positive, what is the probability that you really have the disease? (b) a week later you obtain a second opinion, repeating the test with a different doctor. use the letter s for the event "the second test says you have the disease". you test positive again. given this, what is the probability that you really have the disease? (c) calculate p(s|t) and compare with p(s). are s and t independent? explain.