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  "body": "\n## Definition\n\nA probability space is a triple $(\\Omega, \\mathcal{F}, P)$ with these parts.\n$\\Omega$ is a nonempty set, the [[sample space|0W7NFW23RF]].\n$\\mathcal{F}$ is a [[σ-algebra|04WSW8T3SY]] on $\\Omega$. Its elements are the events.\n$P$ is a [[probability measure|0VGMEBVW1M]] on $(\\Omega, \\mathcal{F})$.\n\n## Remarks\n\nFor one roll of a fair die: $\\Omega = \\{1, \\dots, 6\\}$, $\\mathcal{F}$ is the power set of $\\Omega$, and $P(A) = |A| / 6$.\nA discrete probability space has a countable $\\Omega$, the power set as $\\mathcal{F}$, and $P(A) = \\sum_{\\omega \\in A} p(\\omega)$ for a function $p \\ge 0$ with total sum $1$.\nThe interval $[0, 1]$ with its Borel σ-algebra and the length of intervals as $P$ is a probability space. It models a point chosen uniformly at random in $[0, 1]$.\n\n## Explanations\n\n### L1 human\n\nA probability space puts three things together: what can happen, which questions we can ask about it, and how likely each answer is.\nEvery problem in probability starts, at least in the background, with one probability space.\n",
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