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  "body": "\n## Statement\n\nLet $(\\Omega, \\mathcal{F}, P)$ be a [[probability space|0ZYBZ34RT2]] and let $A, B \\in \\mathcal{F}$ be [[events|00SQGJNRTB]] with $A \\subseteq B$.\nThen $P(A) \\le P(B)$.\nMore precisely, $P(B \\setminus A) = P(B) - P(A)$.\n\n## Remarks\n\nThe proof: $B$ is the disjoint union of $A$ and $B \\setminus A$, so $P(B) = P(A) + P(B \\setminus A)$, and $P(B \\setminus A) \\ge 0$.\nWith $B = \\Omega$, monotonicity gives $P(A) \\le 1$ for each event $A$.\nIf $A$ implies $B$, then $B$ is at least as likely as $A$. For example, \"the die shows $6$\" is at most as likely as \"the die shows an even number\".\n\n## Explanations\n\n### L1 human\n\nA bigger event contains more outcomes, so it cannot be less likely.\nThe chance to draw a heart from a deck is at most the chance to draw a red card, because every heart is red.\n",
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