Maths question from Wildlife Guard exam, 2026 by JKSSB
1. 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's the probability a patient has liver disease if they are alcoholic?
Last updated May 15, 2026
Correct Answer:
Option A —
0.16
To find the probability that a patient has liver disease given that they are an alcoholic, we can use Bayes' Theorem.
1. Identify the given information: Let: L be the event that a patient has liver disease. A be the event that a patient is an alcoholic. From the problem statement, we have: P(L) = 0.12 (12% of patients have liver disease) P(A) = 0.06 (6% of all patients are alcoholics) P(A|L) = 0.08 (8% of patients with liver disease are alcoholics)
2. Apply Bayes' Theorem: We want to find P(L|A), the probability a patient has liver disease given they are an alcoholic:P(L|A) = {P\(A|L) \cdot P(L)}{P(A)}
3. Calculate: Substitute the known values into the formula:$$P(L|A) = \frac{0.08 \cdot 0.12}{0.06} P(L|A) = {0.0096}\{0.06}$$$$P(L|A) = 0.16
The probability that a patient has liver disease if they are an alcoholic is 0.16.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
