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In this paper, a new class of fuzzy random optimization problem called two-stage fuzzy random programming or fuzzy random programming with recourse (FRPR) problem is first presented; then its deterministic equivalent programming problem is characterized. Because the FRPR problems include fuzzy random variable parameters with an infinite support, they are inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, an approximation approach to the fuzzy random variables with infinite supports by finitely supported ones is proposed, which results in finite-dimensional FRPR problems. After that, this paper is devoted to establishing the conditions under which the objective value (optimal objective value, and minimizers) of such finite-dimensional FRPR problem can be shown to converge to the objective value (respectively, optimal objective value and minimizers) of the original infinite-dimensional FRPR problem.