This study developed a two-parameter linear probabilistic model of criterion referenced measurement, which relates an examinee's observed ability to his true ability through a guessing parameter and a carelessness parameter, both of which are probabilities. This model was applied to a survey of 10- and 14-year-old Australian students to estimate the proportion who had been able to master basic skills in mathematics and literacy. The estimates were derived by using a Bayesian inferential procedure incorporating the developed measurement model within a beta-binomial, decision-theoretic framework based on a two-state conception of mastery and non-mastery. The results of a computer simulation of the model indicate that guessing and carelessness may markedly affect the determination of passing scores, and hence the accuracy of decision about mastery. The computer program for calculating cutting scores, posterior probabilities, and prior and posterior distribution statistics is appended. (Author/CTM)