This paper deals with the problem of estimating the size k of a closed animal population from data obtained by sampling one animal at a time, which is marked and then immediately returned to the population. It is assumed that conditional on a capture, each animal i (i=1,...,k) has a fixed probability 0. of being the victim (6 1 +...+6 k =1), which need not be equal for all animals. Since a trapped animal is immediately put back, the above assumption implies that the result of a sequence of captures follows a multinomial distribution with an unknown number of cells which is equal to the population size k, and unknown cell probabilities which correspond to the catch probabilities 6 ...,6 of the animals in the population. This observation is used to derive k a Bayesian method to estimate the population size under various assumptions about available prior information. The estimation method is tested on a fictive population of k = 500 animals with equal catch probabilities 6i = 1/500 (i=1,...,k), as well as on a sample from a population of butterflies.