Question

At a certain? hospital, 50 patients have lung? cancer, 45 patients? smoke, and 40 have lung cancer and smoke. Suppose the hospital contains 250 patients. If a patient chosen at random is known to? smoke, what is the probability that the patient has lung? cancer?

Answer 1

Given that, At a certain? hospital, 50 patients have lung? cancer, 45 patients? smoke, and 40 have lung cancer and smoke. Suppose the hospital contains 250 patients.

If a patient chosen at random is known to? smoke, we want to find the probability that the patient has lung? cancer.

Solution: Of the 30 patients who smoke, 25 have lung cancer.

So if your patient smokes, there is a probability of 25/30= 0.8333 that your patient has lung cancer.

Here, the patient is known to smoke, there are 30 total smokers, and 25 of the smokers have lung cancer.
So, the probability that a random smoker has lung cancer is,

25/30 = 0.8333