Due to the limited capabilities of a single bio-nanomachine, complicated tasks can be performed only with the co-operation of multiple bio-nanomachines. In this work, we consider a diffusion-based molecular communication system with a transmitter bio-nanomachine (TBN) communicating with a fully-absorbing spherical receiver bio-nanomachine (RBN) in the presence of other TBNs. The bits transmitted by each of the TBNs are considered as random in each time slot and different for each TBNs in contrary to the past works in literature with deterministic bits, which are the same to all TBNs. The TBNs are modeled using a marked Poisson point process (PPP) with the location of TBNs as points of PPP, and the transmit bits as marks. In this paper, we derive the expected number of molecules observed at the RBN and the bit error probability of the system. We validate our analysis using numerical results and provide various design insights about the system.