A path diversity is an effective technique to get highly reliable communications in the sensor network. In this paper, the path diversity is examined for a tree network composed of binary symmetric channels (BSC) from the view point of bit error probability (BEP). End-nodes of the network are connected to a fusion center, which sums up the received data. The probability density function (pdf) of decision variable conditioned on a source node data is derived by an iterative algorithm to obtain BEP. Numerical results show that in the case of a majority decision, BEP at the fusion center is almost the same as the BSC crossover probability due to the path diversity effects, even if the number of relay links increases.