This work presents a framework for probabilistic studies on brittle materials undergoing fatigue fracture when geometry and material properties are random independent variables. Benchmark numerical problems are solved to demonstrate the benefits of this framework in studying fracture characteristics. Crack growth is modelled using a phase field approach within a finite element framework. For capturing fatigue fracture, fracture toughness is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function. The number of cycles to failure is treated as the output variable of interest and is estimated within acceptable limits due to the dispersion in random independent properties. The randomness of the output variable is modelled using the polynomial chaos expansion approach. The sensitivity of the input randomness on output responses is determined using Sobol indices. This framework can predict the dispersion in output responses with significantly fewer simulations compared to the Monte Carlo method. The proposed approach is helpful for computationally intensive problems requiring rapid decision-making.