The Condition That Changes Everything

Conditional probability is probability after you learn something new — written P(A | B): the chance of A given that B happened.

Here's the trap: P(A | B) and P(B | A) sound interchangeable and are usually wildly different.

• P(sore throat | flu) is high — most flu patients have one
• P(flu | sore throat) is low — sore throats come from a hundred causes

Swap them and you've made a serious reasoning error — one that regularly shows up in courtrooms.