Why Probability Needs Rules

Probability is not intuition.

It is a mathematical system governed by strict rules called axioms. These rules ensure that probability values are consistent, comparable, and meaningful.

Without axioms, probability collapses into guesswork.


Probability of an Event

The probability of an event is a numerical measure of how likely the event is to occur.

For experiments where all outcomes are equally likely, probability is defined as:

Probability of event A = (Number of outcomes favorable to A) / (Total number of outcomes in the sample space)

Written compactly:

P(A) = favorable outcomes divided by total outcomes

This definition relies entirely on correct counting, which is why the previous lecture was essential.


Basic Properties of Probability

For any event A:

Mathematically:

0 ≤ P(A) ≤ 1