All bows will fire in all five ranged rounds. However, without Archery trained, bows receive a significant penalty to their base chance to hit (CTH) -- 80% penalty, or a total of 20% CTH. This CTH is where you start before calculating effects from dexterity or plus to hit (PTH). With an Archery trained up to an effect of 1.00, you can minimize this penalty and maximize your base CTH. For all bows other than the Elven Long Bow (ELB), this will maximize at 90% CTH (10% penalty) at an Archery of 1.00. The ELB is the only bow that can achieve a full 100% CTH (no penalty) with full Archery trained. The CTH is interpolated linearly when Archery is somewhere between 0.00 and 1.00:
(Archery * 0.8) + 0.2.