Vehicular ad-hoc networks (VANETs) have received a lot of research and industrial attention, including the approval of the IEEE 802.11p standard. However, resource allocation in the standard still makes use of the traditional mechanisms (e.g., carrier sensing) without exploiting the unique characteristics of VANETs. This provides the motivation for this work. As a first step toward the goal and by considering vehicle density, this paper investigates how transmission probability can be determined to optimise throughput of VANETs. A challenging design issue of VANETs is to deal with node (vehicle) mobility, which causes various vehicular densities within the same network and consequently influences the connectivity and capacity of the network. This work shows that it is indeed possible to follow the dynamics of a network and consequently adapt the transmission probability at the MAC layer to reduce the interference and maximise the single-hop throughput between adjacent nodes. By exploiting the characteristics of VANETs, we introduce approximations in order to derive closed-form expressions of the network throughput and other performance metrics in terms of transmission probability, which would otherwise be impossible. Our extensive simulations validate the approximations and the proposed analytical model thus can serve as a promising tool to improve VANETs performance. For example, the optimal transmission probability can be used to develop efficient MAC protocols using vehicle density estimation in VANETs for our future work.