I am following "A Crash Course in Causality: Inferring Causal Effects from Observational Data" on Coursera.
I am struggling at correctly identifying backdoor paths in causal graphs (or DAG for Directed Acyclic Graph).
Example #1 :
The following DAG is given in example in week $2$'s video on the "backdoor path criterion".
The course states that there are $3$ backdoor paths from $A$ to $Y,$ but I see $4$ of them:
\begin{align*} &A \leftarrow W \leftarrow Z \leftarrow V \to Y\\ &A \leftarrow W \to M \to Y\\ &A \leftarrow Z \leftarrow V \to Y\\ &A \leftarrow Z \to W \to M \to Y \quad (\text{not pointed out}) \end{align*}
Example #2 :
In the same week quiz, we are asked to count the number of backdoor paths on this DAG:
Apparently, there is only $1$ but once again I see more of them (I count $2$ of them):
\begin{align*} &G \to A \to B\\ &G \leftarrow E \leftarrow D \to A \to B \end{align*}
Where am I wrong?