Question

At a certain​ hospital, 36 patients have lung​ cancer, 28 patients​ smoke, and 24 have lung cancer and smoke. Suppose the hospital contains 180 patients. If a patient chosen at random is known to​ smoke, what is the probability that the patient has lung​ cancer?

Answer 1

The probability that a patient chosen at random is known to​ smoke, also has lung cancer = 2/15 or 13.3%

Explanation:

1. Let's review the information provided to us to answer this problem correctly:

Number of patients in the hospital = 180

Number of patients that have lung cancer = 36

Number of patients that smoke = 28

Number of patients that have lung cancer and smoke = 24

2. If a patient chosen at random is known to​ smoke, what is the probability that the patient has lung​ cancer?

Let's find out the probabilities of the patients mentioned above:

Probability that a random patient has lung cancer = 36/180 = 1/5

Probability that a random patient smokes = 28/180 = 7/45

Probability that a patient chosen at random is known to​ smoke, also has lung cancer = 24/180 = 4/30 = 2/15 or 13.3%