Alcohol dependency A study of the US clinical population fou

Alcohol dependency. A study of the U.S. clinical population found that 22.5% are diagnosed with a mental disorder, 13.5% are diagnosed with an alcohol-related disorder, and 5% are diagnosed with both disorders.8 What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder? What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder?

Solution

Let

M = mental disorder
A = alcohol related disorder

Thus,

a)

P(M|A) = P(A n M)/P(A) = 0.05/0.135 = 0.37037037 [ANSWER]

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b)

P(A|M) = P(A n M)/P(M) = 0.05/0.225 = 0.222222222 [ANSWER]