A large research hospital has accumulated statistical data on its patients for an extended period. Researchers have determined that patients who are smokers have an 18% chance of contracting a serous illness such as heart disease, cancer, or emphysema, whereas there is only a .06 probability that a non smoker will contract a serious illness. From hospital records the researchers know that 23% of all hospital patients are smokers, while 77% are non smokers. For planning purposes, the hospital physician staff would like to know the probability that a given patient is a smoker if the patient has serious illness.