A method for pseudo-randomly, without bias, selecting instructions for marking in a microprocessor. Responsive to reading an instruction from an instruction cache, an instruction tag associated with the instruction is compared against a pseudo-randomly generated value in a linear feedback shift register (LFSR). If the instruction tag matches the value in the LFSR, a mark bit, indicating the instruction is a marked instruction, is sent with the instruction to an execution unit. Responsive to an indication from the performance monitor, the value in the LFSR is incremented prior to selecting a next instruction to mark. If the value equals a predetermined prime number of increments, the value is reset to all ones to avoid any harmonics with the code stream being executed. Upon receiving the marked instruction, the execution unit combines the marked bit with a selected event and reports the marked event to the performance monitor.