Drinking water may be contaminated by two pollutants. In a given community, the probability that its drinking water contains pollutant A is 0.1, whereas the probability that the drinking water contains pollutant B is 0.2. When pollutant A is present, it will definitely cause health problems, whether or not pollutant B is present. When pollutant B is present, it will cause health problems in only 20% of the population, even when pollutant A is absent. Also, data from similar communities has shown that the presence of the two pollutants is not independent; half of those communities whose drinking water contains pollutant A will also contain pollutant B. If neither pollutant is present, there will be no health problems. A resident is selected at random from this community. Let AE{Presence of pollutant A in the drinking water}, BE{Presence of pollutant B in the drinking water}, HE{Resident has health problems from drinking water}. a] What is the probability that he / she will have health problems from drinking water? b) If the resident is found to have health problems, what is the probability that the drinking water was caused by pollutant A alone? c) If the resident is found to n_ot have any health problems, what is the probability that neither pollutant A nor pollutant B was present in the drinking water