Here we evaluate the concentrations and probabilities of infection for both building interior and exterior exposure sources using a well-mixed model in a connected multizone building. As a central hub of many community and economic activities, buildings provide social connectivity, but the COVID-19 pandemic has reduced social connectivity due to concerns of viral spread within buildings. Although single zone models of infectious spread are well studied, the impact of aerosolized spread of SARS-CoV-2 via air handling systems in multizone buildings remains unexplored. Here we evaluate the influence of filtration, air exchange rates, and the fraction of outdoor air on the probability of infection using the well-known well-mixed modeling approach for a multizone. We find filtration lowers the concentration and probability of infection in both source and connected rooms provided at least some air is recirculated, but that probability is not zero. Filtration has no influence without recirculation or unless the outdoor air contains virus. We find that increasing the air exchange rate removes virus from the source room faster but also increases the rate of exposure to connected rooms. Therefore, slower air exchange rates reduce infectivity in connected rooms at shorter durations, but higher air exchange rates reduce infectivity at longer durations. We further find that when outdoor air is virus free, increasing the fraction of outdoor air is helpful, but, when outdoor air is infective, pathogen exposure inside can persist for hours after a short-term release.