Hospital

Conditional Probability
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)