Question

The probability that a person selected at random from a population will exhibit the symptoms of lung cancer is 0.1. The probability that a person who was found to have the symptoms also has lung cancer is 0.3 and the probability that a person who was found not to have any symptoms also has lung cancer is 0.1. What is the probability that a person has the symptoms, given that they have lung cancer?

Answer 1

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(symptom) = 0.1

P(no symptom) = 1 - 0.1 = 0.9

P(symptoms | lung cancer) = P(symptoms and lung cancer) / P(lung cancer)

= P(symptoms and lung cancer) / [P(symptoms and lung cancer) + P(no symptoms and lung cancer)]

= (0.1x0.3)/(0.1x0.3 + 0.9x0.1)

= 0.25