If a patient chosen at random is known to smoke, what’s the probability they have lung cancer?

Question

At a certain hospital, 45 patients have lung cancer, 35 patients smoke, & 30 have lung cancer & smoke. Suppose the hospital contains 225 patients. If a patient chosen at random is known to smoke, what’s the probability that the patient has lung cancer?

Answer 1

35 patients smoke

30 patients have lung cancer and smoke

30/35 patients have lung cancer given they smoke

probability = 30/35 = 6/7