You are working as a doctor in a clinic. Historic data shows that 11% of the patients entering the clinic have a liver disease. We also know that 23% of the total clinic’s patients are alcoholics. From the patients that are diagnosed with a liver disease, 15% are alcoholics.

If we pick someone who is an alcoholic, what is the probability they have a liver disease?

Hint

Use the Bayes’ Theorem.

Answer

Let’s define

• A = Patient has liver disease
• B = Patient is an alcoholic

So,

• P(A) = 0.11
• P(B) = 0.23

With the Bayes’ Theorem we can now solve this problem as follows:

(1)  

(2)  

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