  Specimens are collected from $N$ different sources. Each specimen has
probability $p$ of being contaminated (e.g., in the case of an infectious
disease, $p$ is the prevalence rate), independently of the other specimens. In
many cases group testing is applicable, namely one can take small portions from
several specimens, mix them together and test the mixture for contamination, so
that if the test turns positive, then at least one of the samples in the
mixture is contaminated.
  In this paper we give a detailed probabilistic analysis of a binary search
scheme, we propose, for determining all contaminated specimens. More precisely,
we study the number $T(N)$ of tests required in order to find all the
contaminated specimens, if this search scheme is applied. We derive recursive
and, in some cases, explicit formulas for the expectation, the variance, and
the characteristic function of $T(N)$. Also, we determine the asymptotic
behavior of the moments of $T(N)$ as $N \to \infty$ and from that we obtain the
limiting distribution of $T(N)$ (appropriately normalized), which turns out to
be normal.
