A hospital's latest survey of its service area shows that 30% of the population receive financial assistance and 20% are smokers. Of those who receive financial assistance, there is a 10% chance they also are a smoker. What is the probability that someone in the population receives financial assistance and is a smoker?

Rationale

The probability that someone in the population receives financial assistance and is a smoker is 0.03.

To find the probability that someone receives financial assistance and is also a smoker, we multiply the probability of receiving financial assistance by the probability of being a smoker given that they receive financial assistance. Thus, 30% (0.30) multiplied by 10% (0.10) equals 0.03.

A (0.02) YOUR ANSWER

This choice suggests a probability of 2%, which arises from incorrectly calculating the product of the probabilities. It may stem from using a different combination of percentages or misinterpreting the relationship between financial assistance and smoking status.

B (0.5) YOUR ANSWER

A choice of 50% indicates a misunderstanding of the percentages provided. This figure does not reflect any calculations from the data, as it exceeds the maximum possible value for a probability and does not align with the provided statistics of financial assistance and smoking rates.

C (0.03) CORRECT

This option accurately represents the probability calculated by multiplying the probability of receiving financial assistance (30%) by the conditional probability of being a smoker among those who receive assistance (10%). Thus, 0.30 * 0.10 = 0.03, which correctly reflects the scenario described.

D (0.05) YOUR ANSWER

Selecting 5% implies an incorrect interpretation of the probabilities. This may arise from mistakenly assuming a higher likelihood of co-occurrence between financial assistance and smoking, without applying the conditional probability as specified in the data.

Conclusion

In summary, the correct probability that a person in the population receives financial assistance and is a smoker is 0.03. This is derived from the logical multiplication of the probabilities given in the survey data. The incorrect answer choices stem from miscalculations or misunderstandings of the conditional relationships presented in the problem.

The probability that someone in the population receives financial assistance and is a smoker is 0.03.

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