Bayes' Rule: Belief Updating

Conditional probability — written P(A | B), 'the probability of A given B' — is the formal version of updating your mind on new information.

P(cough) in the general population might be 2%. P(cough | flu) is far higher — conditioning narrows the world to only the cases where flu holds, then asks how common coughs are inside that world.

The trap that catches everyone: P(A|B) and P(B|A) are wildly different. 'Most people with flu cough' does not mean 'most people who cough have flu' — coughs have a hundred other causes.