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#factorization

2 questions from Probabilistic & Graphical Models

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Question 1: Short answer

mediumAI-checkedProbabilistic & Graphical Models

Binary variables form a chain $A \to B \to C$ : $B$ depends only on $A$ , and $C$ depends only on $B$ . You know $P(A{=}1) = 0.4$ , $P(B{=}1 \mid A{=}1) = 0.7$ , $P(B{=}1 \mid A{=}0) = 0.2$ , $P(C{=}1 \mid B{=}1) = 0.9$ and $P(C{=}1 \mid B{=}0) = 0.3$ . What is $P(A{=}1, B{=}0, C{=}1)$ ?

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