18. 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?
Answer: C
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 a smoker, we multiply the probability of receiving financial assistance by the probability of being a smoker among those who receive financial assistance. This calculation gives us 0.30 (30% financial assistance) multiplied by 0.10 (10% chance of being a smoker), resulting in 0.03.
A) 0.02
This option is incorrect because it underestimates the probability based on the provided statistics. The calculation of 0.30 multiplied by 0.10 yields 0.03, not 0.02.
B) 0.5
This option is incorrect as it suggests a much higher probability than what is supported by the data. The probabilities given (30% for financial assistance and 10% for smokers within that group) do not support a cumulative probability of 0.5.
C) 0.03
This option is correct as it accurately reflects the calculation of the probability that an individual in the population both receives financial assistance and is a smoker. The multiplication of 0.30 and 0.10 gives the correct result of 0.03.
D) 0.05
This option is incorrect because it suggests a higher probability than what the calculations indicate. The correct computation shows that the probability is actually 0.03, not 0.05.
Conclusion
The correct answer is 0.03, which accurately reflects the combined probabilities of receiving financial assistance and being a smoker. All other options fail to represent the correct outcomes based on the provided data, either by miscalculating or misinterpreting the probabilities involved.