Abstract: The probability of success in a Binomial model is often viewed as a continuous random variable when needs to be considered. In this note, we study the mixed Binomial model with the probability of success having the Kumaraswamy distribution. Stochastic orders and dependence in this model are discussed; Further, the new models are employed to fit some real data sets, and the numerical results reveal that KB models perform better than Beta-Binomial model in some occasions.