Bayes rule worked examples
Worked numeric examples of **Bayes’ rule**: updating beliefs when evidence arrives—pairing Course 04 probability with Course 06 uncertainty.
What it is
Worked numeric examples of Bayes’ rule: updating beliefs when evidence arrives—pairing Course 04 probability with Course 06 uncertainty.
Why it matters
Base-rate neglect causes medical and security false confidence. Doing the arithmetic once sticks better than slogans.
How it works (plain)
Prior → evidence likelihoods → posterior. Rare conditions + imperfect tests ⇒ many false alarms even with “accurate” tests.
Everyday example
A disease with 1% base rate and a 99% accurate test still yields many false positives in naive screening stories—compute it.
Try it
Work a 1% base rate, 99% TPR, 5% FPR positive-test posterior with a frequency table (1000 people).
Myths
- ⚠️ Myth: “99% accurate” means 99% posterior after a positive.
- ✓ Reality: Base rates matter.
Sources
- Course 04 probability-basics; Course 06 uncertainty
- Elements of AI: https://www.elementsofai.com/ ↗