Well, a Fate Egg has no real randomness:
If there´s a dragon in the egg, only a dragon can hatch (and not another creature).
The player is only" too stupid" to see the creature in the egg.
I don´t know how things like Photons , another egg, or mammals like Pegasus can come out of eggs, but I think, that´s the magic of Elements .
Growing inside of an egg and hatching is a process over time, so the Egg is

.
That´s my view of it.