In reference to the wet grass / sprinkler Bayesian network problem at this site: http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html
Pr(S=1 | W=1) has been determined as 0.430.
Could someone please help me expand the expression (numerator and denominator) that yields 0.430?
As a try, to begin with ...
Pr(S=1 | W=1) = P(S=1, W=1) / P(W=1) = [P(S=1, W=1 | R=1)P(R=1) + P(S=1, W=1 | R=0)P(R=0) ] / P(W=1)
and then, R depends on C; there is more to denominator for sure.
Help is appreciated!