Mathematics•Medium

Probability & Bayes

Mathematics challenge: Bayes' theorem updates probability estimates when new evidence arrives. A key tool in statistics, medicine, and AI.

Scenario

A medical test for a rare disease has 99% sensitivity and 95% specificity. The disease prevalence is 1%.

Question 1

What is P(+) — the total probability of testing positive?

Question 2

Given a positive test, what is the probability you actually have the disease? (Bayes' theorem)

Question 3

This surprisingly low value (≈17%) despite a near-perfect test is called:

False positive paradoxBase rate fallacyGambler's fallacyConfirmation bias

Question 4

Two fair dice are rolled. P(sum = 7) is:

1/67/361/126/36

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