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Wireless sensor networks have attracted much attention recently with ubiquitous or ad hoc applications. A path diversity is an effective technique to get highly reliable communications in the sensor networks. In this paper, the path diversity is examined for a binary tree network composed of binary symmetric channels (BSCs). 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 is derived by an iterative algorithm to obtain error probability at the fusion center. Numerical results show that in the case of a hard decision, the error probability of the fusion center is almost the same as the BSC crossover probability due to the path diversity effects. Convolutional coding with soft decision Viterbi decoding is also employed to obtain further improvements as well as the path diversity.