Question

Patient medical instruction sheets. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients’ awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. The American Medical Association, however, has found that only 20% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 20% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI sheet?

Short answer

The probability that a person will be hospitalized for a drug-related problem given that the person received the PMI is 0.6.

Step-by-step solution

Important formula

The formula for probability is$\mathbf{P}\mathbf{=}\frac{\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{outcomes}}$

Find the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI.

Here$\mathrm{P}(\mathrm{T}\cap \mathrm{D})=0.12$ and$\mathrm{P}\left(\mathrm{T}\right)=0.2$

$\begin{array}{c}P\left(D|T\right)=\frac{P(T\cap D)}{P\left(T\right)}\\ =\frac{0.12}{0.2}\\ =0.6\end{array}$

Therefore, the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI is 0.6.