In this paper, we introduce new subclasses of analytic and bi-univalent functions connected with a q-confluent hypergeometric distribution by using the Horadam polynomials which, these polynomials, the families of orthogonal polynomials and other special polynomials, as well as their extensions and generalizations, are potentially important in a variety of disciplines in many branches of science, especially in the mathematical, statistical and physical sciences. For more information associated with these polynomials . Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses.