In health area the prevalence rate p is considered to be a fraction that show positive results out of the entire sampled population when tests are done to establish infection of a disease. Tests can be done on individual basis or in a group with individual testing being more costly for large samples of individuals. Using pooled sampling such challenges can be addressed. Group screening was pioneered by Dorfman in 1943 who found it to be more economical in testing blood samples of army inductees to detect syphilis infection. Effective group screening however require choice of optimum values of parameters to guard against obtaining inflated bias in their estimation. Beta distribution was considered as prior distribution in Bayesian estimation of p . When analyzed for group testing the results indicated that Bayes estimates perform much better than maximum likelihood estimates (MLE) especially when prevalence rates are low, while MLE performed better with large values of p . It was also noted that combinations of parameters that lower than the optimum values still resulted in more cost effective performance than individual testing. Key words: Group screening, prevalence rate, optimum values, MLE and Bayes estimate.