Alcohol Dependency . A study of the U.S. clinical population found that 22.5% ar

Question

Alcohol Dependency. A study of the U.S. clinical population found that 22.5% are diagnosed with a mental health disorder, 13.5% are diagnosed with an alcohol-related disorder, and 5% are diagnosed with both disorders.

(a)What is the probability that someone from the clinical population is diagnosed with a mental disorder, given that the person is diagnosed with an alcohol-related disorder?

P(M) = 0.248

(b)What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, given that the person is diagnosed with a mental disorder?

Explanation / Answer

a) P(Diagnosed with a mental disorder | Diagnosed with alcohol - related disorder)

= P(Diagnosed with a mental disorder and alcohol - related disorder)/ P(Diagonsed with alcohol - related disorder)

= 0.05/ 0.135

= 10/27

= 0.3704 (Rounded off to 4 decimal places)

b)

P(Diagnosed with alcohol - related disorder | Diagnosed with a mental disorder)

= P(Diagnosed with a mental disorder and alcohol - related disorder)/ P(Diagnosed with a mental disorder)

= 0.05/ 0.225

= 2/9

= 0.2222 (Rounded off to 4 decimal places)

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