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CFA Level 1
Quantitative Methods

Probability of Disease Given Positive Test

Easy Probability Concepts Bayes Theorem

In a healthcare context, a certain disease affects 1% of the population. A test designed to detect this disease has a sensitivity of 90%, meaning it correctly identifies 90% of those who have the disease. The test also has a specificity of 95%, indicating it correctly identifies 95% of those who do not have the disease.

If a randomly selected individual from the population tests positive for the disease, what is the probability that they actually have the disease? Use Bayes' theorem to calculate this probability.

Hint

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% Correct98%