In order to provide a high quality of care, hospitals usually classify their patients into three categories, namely, i) high-risk, ii) rising-risk, and iii) low-risk patients. High-risk patients make up 5% of the population that will drive the majority of spending in any given year, and they need more help than primary care can offer. Rising-risk patients typically represent 20%ofthe population, while the remaining portion of patients is classified into the low-risk class(75%). A historical dataset from a given hospital shows that 58% of high-risk patients have high blood pressure, where this percentage is 27% for rising-risk and 8% for low-risk patients.

a) What is the probability that a randomly selected patient from this hospital will have high blood pressure?

b) A patient is randomly selected from this hospital. What is the probability that this patient is a high-risk patient?

c) A patient is randomly selected from this hospital and it is found that the patient has high blood pressure. Given that, what is the probability that this patient is a high-risk patient?