Is it likely that a Betta fish will live after jumped out of its tank and got hurt pretty badly?

It is unlikely that a betta fish will survive after jumping out of its tank and getting hurt badly. Betta fish are not known for being able to survive out of water for long periods of time, and even if they do manage to survive the initial fall, they are likely to suffer from severe injuries that could lead to death.

If a betta fish does jump out of its tank, it is important to act quickly. Immediately place the fish back in the tank and observe it closely for signs of distress. If the fish is not swimming normally or is showing any other signs of discomfort, it is important to take it to a veterinarian as soon as possible.