L1

Base Rate Neglect

Junior Quant · Probability & Statistics

Sensitivity99%P(Test+ | Disease)Specificity95%P(Test− | No disease)Prevalence1%P(Disease)A patient tests positive. What is P(Disease | Test+)?

Question

A diagnostic test has 99% sensitivity and 95% specificity. The disease prevalence is 1%. A patient tests positive — what is the probability they have the disease? What changes if prevalence is 10%?