Based on the Bayesian network given below:
https://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html
How would I calculate p(S = T|C = F, R = T, W = F)?
2026-03-25 06:16:19.1774419379
Conditional probability from Bayesian network
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From the diagram $\def\P{\operatorname{\sf P}}\def\T{\operatorname{\mathcal T}}\def\F{\operatorname{\mathcal F}}\P_{C,S,R,W}=\P_C\P_{S\mid C}\P_{R\mid C}\P_{W\mid S,R}$
So using that and Bayes' Rule...
$$\P_{S\mid C,R,W}(\T\mid \F,\T,\F)~{=\dfrac{\P_{S,W\mid C,R}(\T,\F\mid \F,\T)}{\P_{W\mid C,R}(\F\mid\F,\T)}\\[4ex]=\dfrac{\P_{C,S,R,W}(\F,\T,\T,\F)}{\sum_s \P_{C,S,R,W}(\F,s,\T,\F)}\\[4ex]=\dfrac{\P_C(\F)\P_{R\mid C}(\T\mid \F)\P_{S\mid C}(\T\mid \F)\P_{W\mid S,R}(\F\mid \T,\T)~~~}{\P_C(\F)\P_{R\mid C}(\T\mid\F)\sum_s \P_{S\mid C}(s\mid \F)\P_{W\mid S,R}(\F\mid s,\T)}\\[4ex]=\dfrac{\P_{S\mid C}(\T\mid \F)\P_{W\mid S,R}(\F\mid \T,\T)}{\P_{S\mid C}(\F\mid \F)\P_{W\mid S,R}(\F\mid \F,\T)+\P_{S\mid C}(\T\mid \F)\P_{W\mid S,R}(\F\mid \T,\T)}\\[8ex]}$$