Difference between ritual, festival, and ceremony

I am trying draw a line of distinction between these three events.

As I understand it:

Ritual is somewhat related to a religion.
Festival is associated with a group of people and that brings happiness.
Ceremony is something that is followed by a group of individuals before performing a task.

Can someone please tell me if I am wrong, and also provide some examples?

Ceremonies and Rituals can for the most part be interchanged, however most people will associate ceremonies more with organized religion (such as a church service) or events of achievement, such as a graduation ceremony. Rituals seem to give a cultish vibe - or something considered more tribal - such as an ancient Mayan ritual.

Festivals, on the other hand, generally do not have to do with ceremonies or rituals. Festivals are events that people attend in large numbers to have fun. Some examples of festivals are carnivals, fairs, beer-fests, and so on.

Ritual can also mean "a series of actions or type of behavior regularly and invariably followed by someone"; in such case, there is not relation with religions.

Festival can be used to mean "a day or period of celebration, typically a religious commemoration," or "an annual celebration or anniversary." In the first case, the word is related to religions.

Ceremony can mean "a formal religious or public occasion, typically one celebrating a particular event or anniversary," or " the ritual observances and procedures performed at grand and formal occasions." In the first case, also this word is related to religions.