If a person is over the age of 80, there is a 20% chance of having high blood pressure and a 15% chance of having hearing loss. What is the probability a person over the age of 80 has both diagnoses, assuming that the diagnoses are independent of each other?

Rationale

The probability a person over the age of 80 has both diagnoses is 3%.

To find the probability of a person over the age of 80 having both high blood pressure and hearing loss, we can multiply the individual probabilities of these independent events. The calculation involves multiplying 20% (0.20) by 15% (0.15), which results in 0.03 or 3%.

A (15%) YOUR ANSWER

This choice represents the probability of having hearing loss alone, which is 15%. It does not account for the combined probability of both high blood pressure and hearing loss occurring together, making it an incorrect answer.

B (35%) YOUR ANSWER

This option appears to be a miscalculation of the probabilities. It incorrectly adds the probabilities of high blood pressure (20%) and hearing loss (15%), resulting in 35%. Since these events are independent, one cannot simply add the probabilities; therefore, this choice is inaccurate.

C (3%) CORRECT

This is the correct answer. The calculation for the combined probability of both conditions occurring in a person over the age of 80 is 0.20 * 0.15 = 0.03, which translates to 3%. This reflects the likelihood of an individual having both diagnoses simultaneously.

D (5%) YOUR ANSWER

This choice does not represent any meaningful calculation of the two independent probabilities. It incorrectly suggests a higher likelihood of both conditions occurring together without proper mathematical justification, thus making it an incorrect answer.

Conclusion

The probability of a person over the age of 80 having both high blood pressure and hearing loss is calculated as 3%, derived from the multiplication of the independent probabilities of each condition. Understanding how to correctly calculate combined probabilities is essential for accurately interpreting health statistics and probabilities in a clinical context.

If a person is over the age of 80, there is a 20% chance of having high blood pressure and a 15% chance of having hearing loss. What is the probability a person over the age of 80 has both diagnoses, assuming that the diagnoses are independent of each other?

The probability a person over the age of 80 has both diagnoses is 3%.

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