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I'll take a shot at answering.
Question 1: In a galaxy far, far, away, (well, maybe not that far!), the ""Nerd" allele is completely dominant (N) over the "non-nerd" allele (n). What is the probability of 2 heterozygous parents having 2 nerdy kids in a row?"
The answer you got (1/16) isn't the correct answer, but your reasoning was correct minus one detail. In the question, the "Nerd" allele is completely dominant. What does completely dominant mean? Well, Wikipedia explains it very nicely in a single sentence:
"Complete dominance occurs when the phenotype of the heterozygote is completely indistinguishable from that of the dominant homozygote"
What does this mean?
Well, it means that while NN is (obviously) a nerd, the heterozygote Nn is also a nerd as the "heterozygote is completely indistinguishable from that of the dominant homozygote."
Thus, looking at your Punnett square, you will also include the heterozygous Nn to your NN count. So, in the end, with the breeding of heterozygous parents, there will be a 3/4 chance of getting a nerd with every breeding. So, applying your same logic as you initially did, 3/4 x 3/4 gets you 9/16, which is the answer.
You were likely thinking of the allele being "incompletely dominant" (the classic example of a incompletely dominant allele is the red flower/white flower breeding to yield a heterozygous incompletely-dominant pink flower). Nevertheless, great job on figuring out the probability if it was an incompletely dominant allele!
Question 2: The Pedigree
So, pedigrees are interesting little buggers. They require a little bit of logic, luck, and time to think them through. But (for me at least) they're also a little fun. Let's begin:
Before we begin, though, let's straighten one thing out:
1) The brown eye color allele is completely dominant (thus)
1.1) Brown eyes can be: BB or Bb
1.2) Blue eyes must be: bb
Now let's begin (again):
The first one (number 2) is figuring out George's genotype. What do we know?
1) George has brown eyes (can be BB or Bb)
2) George mated with a blue eyed person (bb)
3) George's children have both brown eyes (BB or Bb) and blue eyes (bb).
Now, let's experiment. If George had a BB genotype, and he mated with a "bb" genotypic wife, then his children (through Punnett square) can only be Bb genotype (and phenotypically, only Brown-eyed). However, George has blue eyed children in addition to brown eyed children, so he does not have a BB genotype as BB would only yeild brown eyed children and no blue eyed children. Thus, George is Bb. This enables him to have Bb and bb children (brown and blue eyed respectively).
Tom is a child of George (Bb) and Arlene (bb) and has blue eyes. Since brown eye color is a completely dominant trait, the only way to have the recessive blue eyes is by being homozygous recessive (bb). Thus, Tom is bb in genotype.
Sam is a child of George and Arlene, and Sam has brown eyes (either BB or Bb). However, as shown in the previous section (of George), the children of George (Bb) and Arlene (bb) can only be Bb (brown) and bb (blue). Thus, as Sam is a brown eyed child of George and Arlene, he has the Bb genotype.
Alan is the brown-eyed (BB or Bb) son of Sandra (BB or Bb) and Tom (bb). Alan (BB or Bb) married Tina (BB or Bb) and had a brown eyed child (BB or Bb). Since Sandra's genotype is unknown (BB or Bb) and there is no blue eyed child of Sandra's and Tom's present to confirm a Bb genotype, it is impossible to know Alan's genotype. He could be BB or Bb. His child does not help either has he is an unknown brown-eyed child, too. Thus, not enough information is provided to know for sure Alan's genotype.
The same goes for Christopher. Since Alan's genotype is unknown (BB or Bb) and Tina's genotype is unknown (BB or Bb) and neither of them have had a blue eyed child (only brown-eyed Christopher), is is not possible to determine the genotype of Christopher without more information.
Hope this helped.
May the Force be with You...
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