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  "body": "\n## Definition\n\nLet $E$ be a [[random experiment|0HM05N3FJD]].\nA sample space of $E$ is a nonempty [[set|0SJ3RX9TXA]] $\\Omega$ with two properties.\nEach performance of $E$ gives exactly one element of $\\Omega$.\nEach element of $\\Omega$ is a possible result of $E$.\nThe usual notation for a sample space is $\\Omega$ or $S$.\n\n## Remarks\n\nThe elements of $\\Omega$ are mutually exclusive: two different elements cannot both be the result of one trial. They are also collectively exhaustive: some element is always the result.\nFor one toss of a coin, $\\Omega = \\{H, T\\}$. For two rolls of a die, $\\Omega = \\{1, \\dots, 6\\}^2$ has $36$ elements.\nOne experiment can have more than one sample space. For a card drawn from a deck, $\\Omega$ can be the set of $52$ cards or the set of the $4$ suits.\nA sample space can be finite, countably infinite or uncountable. The time until a lamp fails has the sample space $[0, \\infty)$.\n\n## Explanations\n\n### L1 human\n\nThe sample space is the list of everything that can happen in the experiment.\nFor a die, the list is $1, 2, 3, 4, 5, 6$. Every question about the die is then a question about this list.\n",
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