Disease Prevalence and Test Accuracy - Quant Trader Interview Question
Difficulty: Medium
Category: Conditional Probability
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Topics: Bayesian Update, probability, conditional probability, mental-math
Problem Description
A new diagnostic test for a rare disease has been developed. The test is said to be 99% accurate, meaning it correctly identifies individuals with the disease 99% of the time (sensitivity) and correctly identifies individuals without the disease 99% of the time (specificity). The disease affects 1 in 10,000 people in the general population.
You take the test, and the result comes back positive. What is the approximate probability that you actually have the disease?
Use Bayes' Theorem. Let D b
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