Please let me know if I solved this problem correctly. I had stats many years ago, so I am trying to refresh my math skills. If I didn't solve this problem correctly, please guide me.
Thanks so much for your help!
Problem: 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.
Answer: .23*.18 + .77 * .06=.0876
.23 * .18 / .0876 = .4726