A study of the US clinical population found that 21.2% are diagnosed with a ment
ID: 3071121 • Letter: A
Question
A study of the US clinical population found that 21.2% are diagnosed with a mental disorder, 14.7% are diagnosed with an alcohol-related disorder, and 6% 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
P(mental disorder) = 0.212, P(alcohol-related disorder) = 0.147, P(Both disorders) = 0.06
A)
P(Mental disorder | alcohol related disorder) = P(Both disorders) / P(alcohol-related disorder)
= 0.06 / 0.147
= 0.408
B)
P(Alcohol-related disorder | mental disorder) = P( Both disorders) / P(mental disorder)
= 0.06 / 0.212
= 0.283
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