Poverty is global serious issue which differs in various cultures across the world and over time, varies according to the understanding of the society. Poverty is the level wherein an individual or people do not have the fundamental money-related assets and basics for the least expectation for everyday comforts. Therefore, this study applies a bayesian approach to poverty rates using the wealth index data in the south-western part of Nigeria to examine their poverty levels. The likelihood was Bernoulli and the conjugate Beta distribuitions at five different parameter values [Beta (1, 1), Beta (2, 2), Beta (4, 4), Beta (8, 8) and Beta (10, 10)] were elicited for the prior. Thus, the Beta-Bernoulli posteriors were derived, fitted and their parameters estimated for both the poor data set and the non-poor data set. The result for the poor data showed that as values of the prior parameters increases the posterior mean increases and the posterior variance decreases. So, at Beta (10, 10), the posterior standard variance is the lowest which indicates that about 36% of South-Western Nigeria population are extremely poor. Also, the result for the non poor data shows that as the values of the posterior parameters increases with increase in the prior parameters values, the posterior variance for prior, Beta (1, 1) has the least value 10.78%. This means that about 11% of South-Western Nigeria population are extremely non poor (rich).