# Expected Prediction Error for Classification

I am self-studying elements of statistical learning. I got stuck in the following equations: The expected prediction error for classification is given as:

$$G(x) = argmin_{g \in G} \sum _{k=1}^K L(G_k,g) Pr (G_k|X=x)$$ where L is the loss function, G is the set of possible classes, g is our predictions. Then the book says:

with the 0-1 loss function this fun simplifies to:

$$G(x) = argmin_{g \in G}[1-Pr(g|X=x)]$$

I could not understand the simplification.

$$G(x) = argmin_{g \in G} \sum _{1 \le k \le K,G_{k}\ne g} Pr (G_k|X=x)$$
$$G(x) = argmin_{g \in G}[1-Pr(g|X=x)]$$