From
http://www.labs4rescue.com/faq.htm
"Two sets of genes, not one, control a Lab's coloration. One set of genes controls whether the Lab will be dark (either black or chocolate) or light (yellow). Dark is dominant over light. Thus a Lab whose genotype is EE (homozygous dominant) or Ee (heterozygous) will be dark; only Labs that are ee (homozygous recessive) can be light.
The second set of genes only come into play if the Lab is dark (either EE or Ee). This set controls whether the Lab is black (the dominant trait) or chocolate (the recessive trait). Thus, a dark dog (ie. EE/ Ee) that is BB (homozygous dominant) or Bb (heterozygous) will be black, while the only way a dog can be chocolate is for it to be dark (EE/Ee) AND bb (homozygous recessive).
So now, the possibilities for black dogs are EEBB, EEBb, EeBB, or EeBb. The possibilities for a yellow dog are eeBB, eeBb, or eebb. And the possibilities for a chocolate dog are EEbb or Eebb. Remember that puppies will get one E/e from the dam and one from the sire, as well as one B/b from the dam and one from the sire to make up their complete "code". If you had two parents that were both EeBb (black in appearance), you can get all three colors in the resulting litter! Furthermore, when you realize that a pair of yellows can only give their puppies the ee combination, you understand why two yellows only produce yellows. In a similar fashion, two chocolates can only bequeath bb to their puppies, so two chocolates can never produce a black puppy.
The eebb is an interesting case, as this is a yellow dog with chocolate pigmentation on its nose and eye rims. A dog that is bb always has this pigmentation. Under the current standard, a yellow with chocolate pigmentation is disqualified."
or a Dudley.
So, according to this a EeBb (black) mated to another EeBb (black) has a 6.25% chance of a dudley (25% of 25%).
eeBb (yellow) x EeBb (black) has a 12.5% (50% of 25%)
eeBb (yellow) x eeBb (yellow) has a 25% (50% of 50%)
Eebb (chocolate) x EeBb (black) has a 12.5% (50% of 25%)
Eebb (chocolate) x eeBb (yellow) has a 25% (50% of 50%)
Eebb (chocolate) x Eebb (chocolate) has a 25% (50% of 50%)
or am I doing the math wrong?
(Yes, I enjoythe math)
So, according to another posts, Doc E's dog is eeBB which can never produce a dudley or chocolate. Now if Doc E bred his dog to EEbb (chocolate), the possible combinations are: EeBb (black 100%).
If he bred with a Eebb (chocolate): EeBb (black 50%), eeBb (yellow 50%).
With a eeBB (yellow 100%).
eeBb (yellow) x eeBB = eeBb (yellow 50%), eeBB (yellow 50%)
EEBB (black) x eeBB = EeBB (black 100%)
EEBb (black) x eeBB = EeBB (black 50%), EEBb (black 50%)
EeBB (black) x eeBB = EeBB (black 50%), eeBB (yellow 50%)
EeBb (black) x eeBB = EeBB (black 25%), EeBb (black 25%), eeBB (yellow 25%), eeBb (yellow 25%)
So, in actuallity, breeding with a black lab will produce 2/3 chance for black and 1/3 chance for yellow. (adding up percentages: 300 black, 100 yellow). Breeding with a chocolate would produce 2/3 black and 1/3 yellow (150 black, 50 yellow). And breeding with a yellow will produce only yellows!