38. A hospital's community health needs assessment shows that 20% of the population have heart disease and 15% have a respiratory disease. Of those who have heart disease, there is a 20% chance they also have a respiratory disease. What is the probability that someone in the population has heart disease and a respiratory disease?
Answer: A
The probability that someone in the population has heart disease and a respiratory disease is 0.04.
To find the probability that someone has both heart disease and respiratory disease, we can multiply the probability of having heart disease by the conditional probability of having respiratory disease given heart disease. This results in 0.20 (heart disease) * 0.20 (also having respiratory disease) = 0.04.
A) 0.04
This option is correct because it accurately represents the probability calculated by multiplying the probability of having heart disease (20%) by the probability of having respiratory disease given heart disease (20%). Thus, the calculation yields 0.20 * 0.20 = 0.04.
B) 0.03
This option is incorrect as it does not align with the calculated probability. To achieve a probability of 0.03, one would need to miscalculate the multiplication or incorrectly assess the percentages involved, which in this case does not reflect the actual data provided in the assessment.
C) 0.007
This option is also incorrect. The probability of 0.007 does not represent the correct multiplication of the probabilities given in the context of the problem. The percentages provided lead to a higher probability than 0.007, indicating a misunderstanding of the calculations required.
D) 0.35
This option is incorrect as well, as it significantly overestimates the probability in question. A probability of 0.35 would imply that a large portion of the population suffers from both diseases simultaneously, which contradicts the individual probabilities given (20% for heart disease and 15% for respiratory disease).
Conclusion
In conclusion, the correct answer of 0.04 accurately reflects the joint probability of having both heart disease and respiratory disease based on the provided data. The other options fail to represent the valid calculations or misinterpret the relationships between the diseases, thus reinforcing why 0.04 is definitively the correct choice.