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Recently, Kim (2011) introduced 𝑞-Bernstein polynomials which are different 𝑞-Bernstein polynomials of Phillips (1997). In this paper, we give a 𝑝-adic 𝑞-integral representation for 𝑞-Bernstein type polynomials and investigate some interesting identities of 𝑞-Bernstein type polynomials associated with 𝑞-extensions of the binomial distribution, 𝑞-Stirling numbers, and Carlitz's 𝑞-Bernoulli numbers.