In this paper, we consider random access protocols with MPR, where there is an access point (AP) and multiple nodes in a wireless network. The AP has an M MPRcapability. The study includes both the slotted-Aloha and the -persistent CSMA protocols. For both protocols, each node makes a transmission attempt with a given probability in a generic slot. The goals of this paper are to figure out the relation between the optimal transmissions probabilities for both protocols and, based on the result, to develop a random access protocol which achieves a throughput close to the maximum value in the MPR scenario. We derive the optimal transmission probability in the slotted-Aloha with MPR. Based on the derived optimal transmission probability in the slotted-Aloha protocol with MPR, we provide a simple distributed algorithm for estimating the number of active nodes (i.e., nodes that have packets ready for transmission) at runtime. By observing the number of successful transmissions in a slot, each node can get an estimate of the number of active nodes and use this estimate to tune its transmission probability. To improve the system throughput in the MPR case, we propose a simple -persistent CSMA protocol with MPR, where the transmission probability of a node is dynamically and optimally tuned based on the estimated number of active nodes in the network. The proposed protocol can achieve a system throughput close to the theoretical maximum value.