Probability of an event

Classical definition

Suppose a trial has a finite number of equally likely elementary outcomes (

n

of them). Exactly

m

of them are favorable to event

A

. Then the classical probability is $P(A)=\dfrac{m}{n}.$ Properties: $0\le P(A)\le 1$ ; a certain event has $m=n$ , impossible — $m=0$ .

The key is the equal likelihood assumption; with “heavy” balls the same physical urn is a different model

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