In this paper, we develop a novel mathematical model to estimate the probability distribution function of the number of tags discovered after a certain number of interrogation rounds. In addition, the pdfs of the number of rounds needed to discover all the tags are also calculated. The estimation of such pdfs will be helpful in estimating the number of interrogation rounds and the optimal parameter configuration of the RFID system which in turn will be helpful in estimating the time needed to discover all tags. Our results show that the proposed model accurately predicts the tags detection probability. We then use the proposed model to optimally configure the reader parameters (i.e. the frame size and the number of interrogation rounds).