A medical test for a rare disease has 99% sensitivity and 95% specificity. The disease prevalence is 1%.
Formula Sheet
Bayes: P(A|B) = P(B|A)·P(A) / P(B)P(A∪B) = P(A)+P(B)−P(A∩B)P(A|B) = P(A∩B)/P(B)What is P(+) — the total probability of testing positive?
Given a positive test, what is the probability you actually have the disease? (Bayes' theorem)
This surprisingly low value (≈17%) despite a near-perfect test is called:
Two fair dice are rolled. P(sum = 7) is: