a large research hospital has accumulated statistical data on its patients for a

Question

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 serious illness such as heart disease, cancer, or emphysema, whereas there is only a .06 probability that a nonsmoker will contract a serious illness. from hospital records, researchers know that 23% of all hospital patients are smokers, while 77% are nonsmokers. for planning purposes, the hospital physician staff would like to know the probability that a given patient is a smoker if patient has a serious illness.

Explanation / Answer

D is proability that patient having illness

P(D) = P(smoker) *P(illness) + P(non smoker)*P(illness)

23*.18 + .77 * .06=.0876

P(patient smoker given that he has illness ) = 

P( smoker) * P( thus illness) / P( patient having illness)

.23 * .18 / .0876 = .4726

thus ans

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