State Kolmogorov's three probability axioms.

easy

Answer

$For a sample space Ω and events A: (1) P(A) \geq 0 (non-negativity).$
$(2) P(Ω) = 1 (normalization — some outcome must occur).$
$A_{1}$
$All of probability theory — conditional probability, Bayes, expectation, independence — is derived from these three axioms.$

Check yourself — multiple choice

P(A) can be negative
P(A) ≥ 0; P(Ω) = 1; $P(\;A_{i})\; = \;{\Sigma}$ $P(A_{i})$ for disjoint events — everything else is derived
P(Ω) = 0
Additivity holds without disjointness

Kolmogorov: non-negativity + normalization + countable additivity for disjoint events.

#probability#theory

215 interview questions in this topic.