Lets use X for a dom trait, and O for normal.
Animals have two copies of each gene. During gamete (sperm/egg) production, only one copy of each gene is passed on. Actually one cell splits into 4 gametes technically, but that doesnt matter in this example, so for the sake of making it simpler lets just say one cell forms one gamete.

lets say dad ha OX and mom has XX
Dads sperm will be randomly O or X.
Moms eggs will be X
If dad only formed and released 4 sperm at a time and fertilized 4 eggs in the mother, then the outcome would be guarenteed to be XX, XX, XX, and OX. The problem with that is that dad makes many sperm and out of that group only some fertilize the eggs. Lets say dad makes X, X, X, X, O, O, O, O. That group of sperm follows the "rules" and is half and half. But, only part of that group gets to mom's eggs. That group could be any random group of 4 (to stick with the example, but it would be how every many eggs are fertilized) That means the possible combinations for the genes that make it to the eggs are XXXX, XXXO, XXOO, XOOO, and OOOO. There are more possibilities than that because in XXOO each X could be any of the 4 X's and each O could be any of the 4 O's. That is why its possible for several in a clutch to prove out, or for none of them to prove out. I hope this made sense.

PS, this was meant to go after what is now post #44
in this thread.