i think that every time that the playes breeds a panda it randomly chooses the panda that will come out but i could be wrong and it could be the same as the cats and sheep where if you breed 2 different kinds the baby would be either one of it's parrents
Is it even bad luck if they got a 1/16 roll 5 times in a row? You're looking at a less than 1% chance there.
I'm not 100% sure, but they didn't state what version they were playing on, like an unstable snapshot. Unless it is bugged, I'm not exactly sure the full situation. I'm probably also not the best person to come to with this question, I don't typically play anything higher than 1.8.
Those are the chances for mutations and natural spawning.
Breeding is a lot more complicated.
If I understand the Wiki correctly then when breeding, each panda has 2 genes, one "Main" and one "Hidden".
The baby panda gets one gene from each parent (with a 1/32 chance of the gene mutating) one gene randomly becomes the "Main" gene and the other the "Hidden" gene and with the exception of the Weak and Brown pandas (which need both genes to be the same) the Main gene determines the type.
So presumably at least half of your pandas have a "Hidden" Agressive "gene".