The problem of non-unique cell classification in categorical data arises when the cell that an observation falls in cannot be uniquely identified. This problem is further compounded when data for some of the categories is sparse. We compare two approaches for Bayesian estimation of multinomial cell probabilities in such circumstances. One approach is based on an exact likelihood and the other is based on an augmented data likelihood. The failure of correct chromosome separation (non-disjunction) leads to genetic disorders, such as trisomy 21 which causes Downs Syndrome. For a given nuclear family, it may not be possible to uniquely identify the parental origin of non-disjunction. The methods described above are demonstrated in estimating probabilities of maternal and paternal meiotic non-disjunction. The results are checked against laboratory results obtained using information from numerous gene locations.