The present research concerns the numerical analysis of an uncertain coupled fluid-structure dynamical system, for which the geometrical nonlinearities of the structure induced by the large deformations and the large displacements are taken into account. The structure is coupled with an internal cavity filled with a linear inviscid compressible fluid. The formulation is carried out in terms of displacements and pressure unknowns. The modal basis is made up of the structural modes of the structure and the acoustic modes of the fluid. A nonlinear-reduced order model is then numerically constructed in order to reduce the size of the problem. The uncertainties are then implemented by using the nonparametric probabilistic framework. Note that a peculiar attention that allows the uncertainties on the nonlinear part to be coherently taken into account by preventing the presence of a too large number of random variables used for generating the stochastic model is made. A numerical application is presented.