A new diagnostic test for a certain medical condition was administered to 200 patients. The results are shown in the table. If a patient is selected at random, what is the probability the patient tested negative given that the condition was present?

Rationale

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

To determine this probability, we need to focus on the patients who had the condition and the outcomes of their tests. In this scenario, if 130 patients had the condition and 33 of them tested negative, the probability of selecting a patient who tested negative given the condition is represented by the fraction of negative tests over the total patients who had the condition.

A (33/130) CORRECT

This choice accurately reflects the scenario described. It indicates that out of 130 patients who had the condition, 33 tested negative. Thus, the probability that a randomly selected patient with the condition tested negative is 33 divided by 130.

B (97/130) YOUR ANSWER

This option incorrectly represents the probability of a negative test. Instead, it suggests that 97 patients tested positive out of those 130 patients who had the condition. While it accurately reflects the number of positives, it does not answer the question regarding the negative test outcome.

C (67/200) YOUR ANSWER

This choice fails to take into account the condition of the patients. It represents the number of patients who tested negative out of the total of 200 patients, rather than specifically focusing on those who had the condition. Thus, it does not provide the required conditional probability.

D (33/200) YOUR ANSWER

This option also misrepresents the probability by showing the number of negative tests out of the total 200 patients. Like option C, it does not consider the condition present in the patients, making it irrelevant to the question asked.

Conclusion

The correct calculation of the probability that a patient tested negative given the presence of the condition is crucial for understanding diagnostic test accuracy. In this case, 33 out of 130 patients with the condition tested negative, leading us to conclude that the probability is 33/130. The other options either misinterpret the population or fail to focus on those who actually had the condition, demonstrating the importance of context in probability calculations.

A new diagnostic test for a certain medical condition was administered to 200 patients. The results are shown in the table. If a patient is selected at random, what is the probability the patient tested negative given that the condition was present?

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

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