In randomized response sampling, prior information is of particular value because the randomization effectively reduces the amount of sample information. Warner’s model with a beta prior distribution for the proportion of interest yields posterior distributions that are mixtures of beta distributions. These mixtures are readily interpretable, but approximations that provide beta posterior distributions simplify the analysis. An example indicates that the approximations are quite accurate, provides some insight into the effect of different prior distributions, and demonstrates the practical value of prior information in the attempt to obtain precise estimates when randomized response methods are used. © 1979, Taylor & Francis Group, LLC.