The Power of "Given That"

Probability · Axiom Academy

INTRO The Power of "Given That" See how knowing something changes everything about probability. Imagine 100 random days. Some are cloudy, some have rain. Click the buttons below to see the different types of days. Now, here's the key question: if you wake up and see it's CLOUDY, what's the probability it will rain? In mathematics, we use a special symbol to mean "given that." Let's see how it changes probabilities. P(Disease | Positive Test) - The probability you have the disease GIVEN that your test came back positive. This is very different from just P(Disease)! P(Fraud | Unusual Activity) - The probability a transaction is fraud GIVEN unusual patterns. Security systems use this constantly. P(Like Movie X | Liked Movie Y) - Streaming services use conditional probability to recommend content based on what you've already enjoyed. P(Win | See Card) - In card games, the probability you win changes dramatically based on which cards you can see.

This is the written version of the interactive lesson above. See the full Probability course.