[BobS]

Red hair and blue eyes are more recessive genes than blond genes. I know there are variations. I was using the example of parents that have genes for purely dark eyes and hair and have purely recessive genes for red hair and blue eyes. To simplify the the discussion. You get AA(25%), AB + BA(50%), and BB (25%). John Thune and his wife had 4 to 1 odds against them with their 1st red-haired girl. And I believe 4^2 to 1 odds against them having a second red-haired girl. Am I wrong with the math? Is it 8 to 1 odds for the second child?

[Politicalities]

To simplify the the discussion...

That's the problem. You're oversimplifying. The human genome isn't that simple, and in this case your simplification omits important details.

You're correct in saying that the odds of two parent organisms, each carriers of a recessive gene, giving birth to two offspring that both have the recessive reinforced is 1/4². But that's not 1/8, it's 1/16 :)

But again, human genetics isn't that simple. Another way of looking at it, though still oversimplified, is this: there are two gene locations, one of which specifies either fair hair (F) or dark hair (D), and the other of which specifies either red hair (R) or non-red hair (N). Fair hair is recessive while red hair is dominant. A child who has genes for both fair and red hair will be a redhead.

Suppose John Thune is FD RR, while Kimberley Thune is FF NN. Their chances of having a single redheaded offspring are 50%, and two redheaded offspring are 25%. This, again, is an oversimplification of the actual genome, but is closer to reality than the 6.7% you came up with.