For a particular pain clinic we know the following information:

10% of patients are prescribed narcotic pain killers.
Overall, 5% of the clinic's patients are addicted to narcotics (including pain killers and illegal substances).
Out of all the people prescribed pain pills, 8% are addicts.

Use Bayes Theorem (given below) to provide an answer to the question: "if a patient is an addict, what is the % probability that they will be prescribed pain pills"?

Note: Provide your answer as a percentage correct to 1 decimal place and do not include the % sign in the answer field.

Question

For a particular pain clinic we know the following information:

10% of patients are prescribed narcotic pain killers.
Overall, 5% of the clinic's patients are addicted to narcotics (including pain killers and illegal substances).
Out of all the people prescribed pain pills, 8% are addicts.

Use Bayes Theorem (given below) to provide an answer to the question: "if a patient is an addict, what is the % probability that they will be prescribed pain pills"?

Note: Provide your answer as a percentage correct to 1 decimal place and do not include the % sign in the answer field.

BlackTom AI · Accepted Answer

We are given the following probabilities: P(Pain pills) = 0.10, P(Addicted) = 0.05, and P(Addicted | Pain pills) = 0.08. 
First, recall Bayes theorem in this context: P(Pain pills | Addicted) = [P(Addicted | Pain pills) * P(Pain pills)] / P(Addicted).
Compute the numerator: P(Addicted | Pain pills) * P(Pain pills) = 0.08 × 0.10 = 0.008. 
The denominator is P(Addicted) = 0.05. 
Divide the numerator by the denominator to obtain P(Pain pills | Addicted) = 0.008 / 0.05 = 0.16. 
Convert to a percentage: 0.16 corresponds to 16.0 when expressed as a percentage with one decimal place, and without the percent sign as requested. 
Thus, the requested value is 16.0.

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