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Probability of smokers: hospital case

A large research hospital has accumulated statistical data on its patients for an extended period of time. 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 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 a serious illness.

Solution Preview

Prob(disease | smoker) = 0.18
Prob(disease | nonsmoker) = 0.06

In the hospital,
Prob(smoker) = 0.23
Prob(nonsmoker) = 0.77

By definition of Conditional ...

Solution Summary

This shows the steps and solution to calculating the probability that a given patient in a hospital (given statistical data) is a smoker if their have a serious illness.