The set T of all categories in a population of RFID tags is estimated within a specified error bound. For each of one or more frames, a reader broadcasts a probability p, a multiplicity d, a frame size M, and a seed value R to the present tags. A deterministic algorithm on each tag, and known to the reader, calculates (i) whether the tag will transmit in this frame, and, if so, (ii) in which slots the tag will transmit a single “1.” When the tags have responded, the reader calculates set T by initially assuming that all possible categories are in set T and then eliminating those categories that would have transmitted in those slots in which no tag transmitted. Alternatively, the reader initially assumes that set T is empty, and adds those categories that would have transmitted in those slots in which one or more tags did transmit.