X is dependent on A and B, $P(X|A,B)$ is given along with $P(X|A,!B)$ , how do you find $P(X|A)$

Question

In a Bayasian network would look like this,

A---,    ____
    |--->|X | 
    |--->|__|    
B --|

Answer 1

If the DAG is as follows: $$A\lower{2ex}{\searrow\lower{2ex}{X}\swarrow}B$$

Then the factorisation gives: $$\mathsf P(X\mid A)=\mathsf P(X\mid A,B)\mathsf P(B)+\mathsf P(X\mid A,{!}B)(1-\mathsf P(B))$$