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  "body": "\n## Statement\n\nLet $(\\Omega, \\mathcal{F}, P)$ be a probability space and let $A, B \\in \\mathcal{F}$ with $0 \u003c P(B) \u003c 1$. Let $B^c = \\Omega \\setminus B$.\nThen\n$$P(A) = P(A \\mid B) \\, P(B) + P(A \\mid B^c) \\, (1 - P(B)).$$\n\n## Remarks\n\nThis is the [[law of total probability|0E5G5FMT2R]] for the partition $\\{B, B^c\\}$, together with $P(B^c) = 1 - P(B)$.\nThe formula is the denominator of [[Bayes' theorem|0NM6E9VW04]] in the case of two hypotheses.\n\n## Explanations\n\n### L1 human\n\nEither $B$ happens or it does not.\nSo the chance of $A$ is its chance when $B$ happens times $P(B)$, plus its chance when $B$ does not happen times $1 - P(B)$.\n",
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