While studying universal constructions on principal bundles, I've stuck on a quite a basic question, namely:

For any Lie group $G$, are there principal $G$-bundles whose holonomy group is $G$?

I suppose the answer is yes, but I have no idea of how to prove it.

While studying universal constructions on principal bundles, I've stuck on a quite a basic question, namely:

Given a Lie group $G$, does there exist a principal $G$-bundle $\pi \colon P \to B$, for some base $B$, that admits a connection $\theta$ whose holonomy group is the full group $G$?

I suppose the answer is yes, but I have no idea of how to prove it.