  Let $X$ be a set of items of size $n$ , which may contain some defective
items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test}
refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive)
if $Q$ contains at least one defective item, i.e., $Q\cap I \neq \emptyset$,
and $0$ (negative) otherwise. We give a novel approach to obtaining tight lower
bounds in non-adaptive randomized group testing. Employing this new method, we
can prove the following result. Any non-adaptive randomized algorithm that, for
any set of defective items $I$, with probability at least $2/3$, returns an
estimate of the number of defective items $|I|$ to within a constant factor
requires at least $\Omega({\log n})$ tests. Our result matches the upper bound
of $O(\log n)$ and solves the open problem posed by Damaschke and Sheikh
Muhammad.
