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?

Rationale

0.04

To find the probability that someone in the population has both heart disease and a respiratory disease, we use the formula for joint probability. This is calculated by multiplying the probability of having heart disease (20%) by the conditional probability of having respiratory disease given heart disease (20% of those with heart disease). Thus, 0.20 * 0.20 = 0.04, or 4%.

A (0.04) CORRECT

This choice correctly reflects the calculation for the probability of an individual having both heart disease and respiratory disease. By multiplying the probability of heart disease (0.20) by the probability of having respiratory disease given heart disease (0.20), we arrive at the joint probability of 0.04.

B (0.03) YOUR ANSWER

This value does not correctly represent the probability of having both diseases. It may arise from a miscalculation or misunderstanding of how to apply the conditional probability to the given percentages, particularly not accounting for the proper multiplication of probabilities.

C (0.007) YOUR ANSWER

This choice significantly underestimates the joint probability calculation. It suggests a misunderstanding of the relationship between the two probabilities or incorrectly applying an incorrect method for determining the joint probability.

D (0.35) YOUR ANSWER

This option is much too high and likely results from incorrectly summing probabilities rather than calculating the joint probability. It does not reflect the actual chance of having both diseases as defined by the problem's parameters.

Conclusion

The correct probability that an individual in the population has both heart disease and respiratory disease is 0.04, derived from multiplying the probabilities of each condition. Understanding how to compute joint probabilities is crucial in health assessments, enabling accurate evaluations of community health needs. The incorrect answers illustrate common pitfalls in applying probability rules, emphasizing the importance of precise calculations and interpretations.

0.04

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test