Answer :

The correct answer is 1) 0.975. To calculate the probability of a person actually having a disease despite testing positive, one needs to consider the test's sensitivity and specificity, as well as the prevalence of the disease in the population. This avoids the base rate fallacy and yields the positive predictive value (PPV), which more accurately represents the likelihood of being diseased given a positive test result.

To address the original question about the probability of a biologist being actually positive with a disease given that 99% of infected patients test positive, we must consider both the probability of the test being accurate and the base rate of the disease. Medical tests are usually characterized by their sensitivity and specificity. Sensitivity refers to the test's ability to correctly identify those with the disease (true positives), while specificity refers to correctly identifying those without the disease (true negatives). Misinterpretation of these values can lead to the base rate fallacy.

To visualize the concept, let's take an example where a test for Diseasitis reads as positive 97.5% of the time. The probability that a person has Diseasitis given that they tested positive can be much lower if the prevalence of the disease is low in the population. If the test also has a certain rate of false positives, for example, incorrectly indicating Diseasitis in healthy patients 30% of the time, and there are many more healthy individuals than sick ones, the probability of actually having Diseasitis despite the positive test result decreases.

In a more comprehensive scenario, suppose we have 20 sick and 80 healthy students. If 10% of the sick students get false negatives, and 70% of the healthy students get true negatives, then among those with negative results, only a small fraction actually have the disease.

The chances of being a true positive rather than a false positive can be calculated using the formula: Number of true positives / Total number of positive identifications. In this context, if 97.5 out of 100 patients test positive, the probability of being a true positive is 97.5% (0.975). The correct answer is 1) 0.975.

Thanks for taking the time to read Suppose a test for some disease reads as positive 97 5 1 0 975 2 0 025 3 0 975 0 025 4 0 025. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada