  We study the detection error probability associated with a balanced binary
relay tree, where the leaves of the tree correspond to $N$ identical and
independent detectors. The root of the tree represents a fusion center that
makes the overall detection decision. Each of the other nodes in the tree are
relay nodes that combine two binary messages to form a single output binary
message. In this way, the information from the detectors is aggregated into the
fusion center via the intermediate relay nodes. In this context, we describe
the evolution of Type I and Type II error probabilities of the binary data as
it propagates from the leaves towards the root. Tight upper and lower bounds
for the total error probability at the fusion center as functions of $N$ are
derived. These characterize how fast the total error probability converges to 0
with respect to $N$, even if the individual sensors have error probabilities
that converge to 1/2.
