  We examine how the measure and the number of vertices of the convex hull of a
random sample of $n$ points from an arbitrary probability measure in
$\mathbf{R}^d$ relates to the wet part of that measure. This extends classical
results for the uniform distribution from a convex set [B\'ar\'any and Larman
1988]. The lower bound of B\'ar\'any and Larman continues to hold in the
general setting, but the upper bound must be relaxed by a factor of $\log n$.
We show by an example that this is tight.
