re: drone paternity @cravenr
Well, a drone is from an unfertilised egg, so by definition it is very much the mother's sole input, as you say, it has no dad, but does have a granddad.
His* mother will be from the genes of her mum and dad in about equal measure. All other things being equal, this would be reflected in her unfertilised eggs. Eggs don't really split along the lines of "dad's eggs" and "mum's eggs" it all gets a bit mixed up – look at meiosis for a long explanation. So, a drone's DNA is about half is his grandfather and about half his grandmother, the same proportions, roughly, as his mum. Nobody else has been able to sneak a gene in there. NOTE – this is NOT in any way cloning, a drone is not a clone of his mum.
With you there is the mixing of your mum (half her dad and half her mum) and your dad (half his mum and half his dad), each combination will come with copying errors, known as mutations. So you are not quite half your mum and half your dad, but very close. Take your dad out of that, and you are left with your maternal grandparents plus whatever mutations sneaked in. That's how it works for drones.
Even then there's a lot that’s the same, so vast numbers of genes will be identical in your mum and dad, and indeed everyone on the face of the planet. I can't recall which one it is (I think it codes a DNA structural protein) but there is a gene that has practically the same base sequence in every human, mammal, chordate, animal, and indeed eukaryote. So when you eat your salad later the exact same DNA sequence (give or take a few base paris) will be in your lettuce as is in you.
I don't know how phenotypes work in bees regarding coloration, but I would guess it's not necessarily the case that "black striped grandmother = black striped drone". Many phenotypes are quite subtle and inter-dependent on genes arriving together, or even the environment. Hydrangea flower colours are a good example of the latter – being soil pH dependent.
Does that help?
*male pronoun used for convenience.