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  "body": "\n## Summary\n\nThe probability axioms of Kolmogorov are the three rules that a probability function $P$ on the events of a sample space $\\Omega$ must obey.\nFirst, $P(A) \\ge 0$ for each [[event|00SQGJNRTB]] $A$.\nSecond, $P(\\Omega) = 1$.\nThird, for each sequence $A_1, A_2, \\dots$ of pairwise disjoint events, $P\\left(\\bigcup_{n} A_n\\right) = \\sum_{n} P(A_n)$. This is countable additivity.\nA function that obeys these rules is a [[probability measure|0VGMEBVW1M]].\n\n## Remarks\n\nAndrey Kolmogorov stated these axioms in 1933.\nThe other rules of probability follow from the axioms. Examples are $P(\\varnothing) = 0$, $P(A) \\le 1$, the rule for the complement and the addition rule for two events.\n\n## Explanations\n\n### L1 human\n\nThe axioms say three things: a probability is never negative, something always happens, and the probabilities of events that cannot happen together add up.\nFor a fair coin, $P(\\{H\\}) = P(\\{T\\}) = 1/2$, and $P(\\{H, T\\}) = 1/2 + 1/2 = 1$.\n",
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