A wireless passive sensor network is a network which, by letting separate RF sources supply energy to sensor nodes, is able to live an eternal life without batteries. Against expectations about an eternal life, however, a wireless passive sensor network still has many problems; scarcity of energy, non-simultaneity of energy reception and data transmission and inefficiency in resource allocation. In this paper, we focus on a wireless passive sensor network providing a packet service which is tolerable to packet losses but requires timely delivery of packets. Perceiving the practical constraints, we then consider a contending-type MAC scheme, rooted in framed and slotted ALOHA, for supporting many sensor nodes to deliver packets to a sink node. Next, we investigate the network-wide throughput achieved by the MAC scheme when the packets transmitted by geographically scattered sensor nodes experience path losses hence capture phenomena. Especially, we derive an exact formula of network-wide throughput in a closed form when 2 sensor nodes reside in the network. By controlling design parameters, we finally optimize the contending-type MAC scheme as to attain the maximum network -wide throughput.Keywords : wireless passive sensor network, MAC, framed and slotted ALOHA, capture, throughput