  This paper addresses the rumor source identification problem, where the goal
is to find the origin node of a rumor in a network among a given set of nodes
with the rumor. In this paper, we focus on a network represented by a regular
tree which does not have any cycle and in which all nodes have the same number
of edges connected to a node. For this network, we clarify that, with quite
high probability, the origin node is within the distance 3 from the node
selected by the optimal estimator, where the distance is the number of edges of
the unique path connecting two nodes. This is clarified by the probability
distribution of the distance between the origin and the selected node.
