Conventional on-demand route discovery methods in Mobile Ad hoc Networks (MANET) employ blind flooding, where a mobile node blindly rebroadcasts received Route Request (RREQ) packets until a route to a particular destination is established. This can potentially lead to high channel contention, causing redundant retransmissions and thus excessive packet collisions in the network. Such a phenomenon induces what is known as broadcast storm problem, which has been shown to greatly increase the network communication overhead and end-to-end delay. In this paper, we show that the deleterious impact of such a problem can be reduced if measures are taken during the dissemination of RREQ packets. We propose two new probabilistic methods for on-demand route discovery, that is simple to implement and can significantly reduce the overhead involved in the dissemination of RREQs. Our analysis reveals that equipping AODV with probabilistic route discovery can result in significant performance improvements on all the standard metrics.