John,
Putting it simply, a queen has a genetic make up that comes half from a
random assortment of her mother's and half from all of her single father.
Her father's genes came from a random assortment of his mother's.  However,
you as a beekeeper assess the genetic qualities of a queen by looking at her
daughters and their activities.  Unless you are into artificial insemination
with single drones the queen will have mated with up to 20 drones, many of
which will have had different mothers.  Even if they came from the same
mother they will have a different random selection of her genes.  Each worker
will therefore have a random selection of her mother's genes plus a full dose
of genes from just one of the many drones she mated with (1 sperm to 1 egg).
Having read the above I am not sure that I did put it simply.  I drew a
diagram before typing.  Perhaps readers might find it helpful to put the
words into a picture.
Chris Slade