juniorProbability
What is probability and how is it formally defined?
Updated May 17, 2026
Short answer
Probability is a measure of the likelihood of an event occurring, defined on a sample space with values between 0 and 1.
Deep explanation
Probability is formally defined using Kolmogorov’s axioms: non-negativity, normalization (P(Ω)=1), and countable additivity. It provides a mathematical framework to quantify uncertainty. Events are subsets of a sample space, and probability assigns each event a value between 0 and 1.
Real-world example
Estimating the probability of rain based on historical weather data.
Common mistakes
- Thinking probability must be based only on intuition rather than mathematical definition.
Follow-up questions
- What are Kolmogorov’s axioms?
- What is a sample space?