A study of the US clinical population found that 22.7% are diagnosed with a ment

Question

A study of the US clinical population found that 22.7% are diagnosed with a mental disorder, 13.6% 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, knowing that the person is diagnosed with an alcohol-related disorder? Please use 3 decimal places.

_______

(b) 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? Please use 3 decimal places.

_______

Explanation / Answer

a)

Probability that population diagnosed with an mental disorder is 0.227

Given that person already diagnosed with alcohol related disorder, we have to find probability that person is

diagnosed with metal disorder = 0.05 / 0.136 = 0.368

b)

Probabilty that the person is diagnosed with a mental disorder = 0.227

We already know that person having alcohol related disorder, then

p(diagnosed with alcohol related disorder/ dignosed with mental disorder) = 0.05 / 0.227

= 0.220

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