Americas
Europe
126SE
Expert-verifiedPatient 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?
The probability that a person will be hospitalized for a drug-related problem given that the person received the PMI is 0.6.
The formula for probability is ${\mathbf{P}}{\mathbf{=}}\frac{\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{outcomes}}$
Here $\mathrm{P}\text{\hspace{0.17em}}(\text{\hspace{0.17em}}\mathrm{T}\cap \mathrm{D}\text{\hspace{0.17em}})=0.12$ 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.
Is a product “green”? A “green” product (e.g., a productbuilt from recycled materials) is one that has minimal impact on the environment and human health. How do consumers determine if a product is “green”? The 2011
ImagePower Green Brands Survey asked this question of more than 9,000 international consumers. The results are shown in the following table.
Reason for saying a product is green | Percentage of consumers |
Certification mark on label | 45 |
Packaging | 15 |
Reading information about the product | 12 |
Advertisement | 6 |
Brand we site | 4 |
Other | 18 |
Total | 100 |
a. What method is an international consumer most likely to use to identify a green product?
b. Find the probability that an international consumer identifies a green product by a certification mark on the product label or by the product packaging.
c. Find the probability that an international consumer identifies a green product by reading about the product or from information at the brand’s Web site.
d. Find the probability that an international consumer does not use advertisements to identify a green product.
Evaluating the performance of quality inspectors. The performance of quality inspectors affects both the quality of outgoing products and the cost of the products. A product that passes inspection is assumed to meet quality standards; a product that fails inspection may be reworked, scrapped, or reinspected. Quality engineers at an electric company evaluated performances of inspectors in judging the quality of solder joints by comparing each inspector’s classifications of a set of 153 joints with the consensus evaluation of a panel of experts. The results for a particular inspector are shown in the table. One of the 153 solder joints was selected at random.
Committee’s judgment joint | Joint Acceptable | joint Rejectable |
Joint Acceptable | 101 | 10 |
joint Rejectable | 23 | 19 |
a. What is the probability that the inspector judged the joint to be acceptable? That the committee judged the joint to be acceptable?
b. What is the probability that both the inspector and the committee judged the joint to be acceptable? That neither judged the joint to be acceptable?
c. What is the probability that the inspector and the committee disagreed? Agreed?
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