After conducting a blood test, the doctor told you that you were tested positive for a fatal disease. Worse, the test is quite accurate: the probability of false-positive (one is tested positive without the disease) is 0.05, and the probability of false-negative (one is tested negative with the disease) is 0.02. Seeing that you are desperate, the doctor told you that overall the disease is rather rare, only 1 in 10,000 people. (a). What is the chance now that you have the disease? (b). Naturally, the doctor orders a retest on you. The result of the second independent test is still positive. What is now your chance of having the disease? (c). If you have done a total of k independent tests, and the results are all positive (quite depressive indeed!), what is your chance of having the disease, expressed in k?