If Peccei-Quinn (PQ) symmetry is broken after inflation, the initial axion angle is a random variable on cosmological scales; based on this fact, estimates of the relic-axion mass density give too large a value if the axion mass is less than about 10 to the -6th eV. This bound can be evaded if the universe underwent inflation after PQ-symmetry breaking and if the observable universe happens to be a region where the initial axion angle was atypically small. Consideration of fluctuations induced during inflation severely constrains the latter alternative is shown.