{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "0464Z0JP2E"
    },
    {
      "field": "uses",
      "target": "0BZQ6ZX584"
    },
    {
      "field": "uses",
      "target": "0DAX8PMAJ4"
    },
    {
      "field": "uses",
      "target": "0EGSEE9J9R"
    },
    {
      "field": "uses",
      "target": "0FJB06AD2P"
    },
    {
      "field": "uses",
      "target": "0GCVEV6BJA"
    },
    {
      "field": "uses",
      "target": "0P0MZ4X682"
    },
    {
      "field": "uses",
      "target": "0PQEBTYDZM"
    },
    {
      "field": "uses",
      "target": "0R46A1XY60"
    },
    {
      "field": "uses",
      "target": "0T6WS7TT77"
    }
  ],
  "body": "\n## Definition\n\nLet $\\Omega$ be a [[sample space|0W7NFW23RF]] and let $\\mathcal{F}$ be a [[σ-algebra|04WSW8T3SY]] on $\\Omega$.\nAn event is an element of $\\mathcal{F}$, that is, a [[subset|0FE8Q5S42Y]] $A \\subseteq \\Omega$ with $A \\in \\mathcal{F}$.\nThe event $A$ occurs in a trial when the outcome $\\omega$ of the trial satisfies $\\omega \\in A$.\n\n## Remarks\n\nWhen $\\Omega$ is finite or countable, one usually takes $\\mathcal{F}$ to be the power set of $\\Omega$. Then each subset of $\\Omega$ is an event.\nFor uncountable $\\Omega$, such as $\\Omega = \\mathbb{R}$, one cannot in general give a probability to each subset. So only the sets in $\\mathcal{F}$ are events.\nThe set operations have probabilistic names: $A \\cup B$ is \"$A$ or $B$\", $A \\cap B$ is \"$A$ and $B$\", and $\\Omega \\setminus A$ is \"not $A$\". The empty set is the impossible event, and $\\Omega$ is the sure event.\nTwo events $A$ and $B$ are mutually exclusive when $A \\cap B = \\varnothing$.\n\n## Explanations\n\n### L1 human\n\nAn event is a statement about the result of the experiment that is either true or false after the experiment.\nFor a die, \"the result is at least $5$\" is the event $\\{5, 6\\}$. It happens when you roll a $5$ or a $6$.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "031TPJVS74",
    "kind": "definition",
    "msc": [
      "60A05"
    ],
    "name": "Event",
    "sources": [
      {
        "locator": "Events in probability spaces",
        "url": "https://en.wikipedia.org/wiki/Event_(probability_theory)"
      }
    ],
    "tag": "00SQGJNRTB",
    "uses": [
      "0W7NFW23RF",
      "04WSW8T3SY",
      "0FE8Q5S42Y"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/00SQGJNRTB/",
  "links": [
    {
      "field": "defines",
      "target": "031TPJVS74"
    },
    {
      "field": "uses",
      "target": "0W7NFW23RF"
    },
    {
      "field": "uses",
      "target": "04WSW8T3SY"
    },
    {
      "field": "uses",
      "target": "0FE8Q5S42Y"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/00SQGJNRTB.md",
  "msc": [
    "60A05"
  ],
  "name": "Event",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/00S/00SQGJNRTB.md",
  "status": null,
  "tag": "00SQGJNRTB",
  "uri": "m2://00SQGJNRTB",
  "url": "https://math2.tamnd.com/wiki/event-definition/",
  "writing": {
    "tag": "00SQGJNRTB",
    "kind": "definition",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "one example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge not_instance_of in",
        "note": "one non-example that fails one clause",
        "have": 0,
        "want": 1
      }
    ]
  }
}