Medical cases histories indicate that different illnesses may produce identical symptoms. Suppose a particular set of symptoms, "H" occurs only with probabilities 0.01, 0.005 and 0.02, respectively. The probability of developing the symptoms H, given illness A, B and C are 0.90, 0.95 and 0.75, respectively. Assuming that an ill person shows symptoms H, what is the probability that a person has illness A?