In VANETs, there are many applications that use broadcast communication as a fundamental operational tool, in disseminating information of interest to other road users under the umbrella of both safety and entertainment applications. Recently, the probabilistic broadcasting scheme is suggested as an efficient broadcast approach. Although a number of probabilistic schemes found in the literature, they still suffer from a high level of rebroadcast redundancy, which often leads to the Broadcast Storm Problem (BSP). Thus, in this paper a new efficient probabilistic broadcast scheme is developed, to target both achieving a high delivery ratio and reducing broadcast redundancy. Using simulation experiment, we compared the performance of the proposed scheme against the recent well known probabilistic schemes and our results confirm the superiority of our scheme over existing schemes in terms of key performance metrics, namely Reachability (RE) and Saved Rebroadcast (SR).