Question 41

The probability the patient tested negative given that the condition was present is 33/130.

This probability represents the likelihood of a patient testing negative while actually having the condition, which is calculated as the number of patients who tested negative among those who truly have the condition.

A) 33/130

This option accurately reflects the probability of a patient testing negative given that they have the condition. It represents the ratio of patients who tested negative (33) to those who have the condition (130), making it the correct choice.

B) 97/130

This choice incorrectly indicates the probability of testing positive among those who have the condition. While it uses the correct denominator (130), it reflects the number of patients who tested positive rather than negative, thus making it incorrect for the question asked.

C) 67/200

This option represents the overall probability of a patient testing negative out of the total number of patients (200). However, it does not consider the specific condition being present, making it irrelevant to the question which focuses exclusively on those with the condition.

D) 33/200

This choice suggests the probability of a patient testing negative out of the total population of 200 patients. Similar to Option C, it fails to address the specific scenario of selecting a patient with the condition, rendering it incorrect.

Conclusion

Option A is definitively correct as it specifically addresses the probability of testing negative among those who have the condition, which is essential for understanding the diagnostic test's effectiveness. The other options either misinterpret the scenario or fail to focus on the relevant patient group, highlighting the importance of contextual accuracy in probability assessments.