  We study a basic problem of approximating the size of an unknown set $S$ in a
known universe $U$. We consider two versions of the problem. In both versions
the algorithm can specify subsets $T\subseteq U$. In the first version, which
we refer to as the group query or subset query version, the algorithm is told
whether $T\cap S$ is non-empty. In the second version, which we refer to as the
subset sampling version, if $T\cap S$ is non-empty, then the algorithm receives
a uniformly selected element from $T\cap S$. We study the difference between
these two versions under different conditions on the subsets that the algorithm
may query/sample, and in both the case that the algorithm is adaptive and the
case where it is non-adaptive. In particular we focus on a natural family of
allowed subsets, which correspond to intervals, as well as variants of this
family.
