A system for formal verification of bounded fairness properties of pseudo random number generators and arbiters that use random priority-based arbitration schemes. The formal verification system determines an upper bound of a request-to-grant delay of an arbiter in terms of a number of complete random sequences. The formal verification system also determines, in terms of a number of clock cycles, an upper bound and a lower bound of a length of a complete random sequence in the random number sequence generated by a random number generator used by the arbiter. The formal verification system then determines a worst case request-to-grant delay bounds of the arbiter system, in terms of a number of clock cycles, by combining the upper bound of the request-to-grant delay of the arbiter with the upper bound of the length of the complete random sequence and the lower bound of the length of the complete random sequence.