At a doctor's clinic, 8% of patients with liver disease are alcoholics. 6% of all patients are alcoholics, and 12% have liver dis…

Question

At a doctor's clinic, 8% of patients with liver disease are alcoholics. 6% of all patients are alcoholics, and 12% have liver disease. What is the probability that a patient has liver disease given they are alcoholic?

1. A. 0.16 (Correct answer)
2. B. 0.44
3. C. 0.016
4. D. 0.22

Correct Answer

Option A — 0.16

Detailed Solution & Explanation

The correct answer is 0.16.

Key Points

• Using Bayes' theorem: P(liver|alcoholic) = P(alcoholic|liver) × P(liver) / P(alcoholic) = (0.08 × 0.12) / 0.06 = 0.0096 / 0.06 = 0.16.