#exact-inference

A fire alarm $A$ goes off because of a fire $F$ or a defective alarm $D$, and a fire is caused by burnt cooking $B$ or flammable chemicals $C$: the edges are $B \to F$, $C \to F$, $F \to A$, $D \to A$. All variables are binary; $B$, $C$, $D$ are 1 with probability $1/2$ each. A node with $k$ parents is 0 if all its parents are 0, and otherwise is 1 with probability $1 - \frac{1}{2i}$ when exactly $i$ of its parents are 1. What is $P(B = 1 \mid A = 1)$?