A study of US clinical population found that 23.4% are diagnosed with a mental disorder, 12.2% 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.
Please explain all steps.