Final answer:
The inheritance of blue color in Smurfs is likely a dominant trait, similar to Mendel's violet flowers. The foot size inheritance could be incomplete dominance or codominance, and the big-footed, white Smurf could potentially have a genotype of 'Bb' for these traits.
Step-by-step explanation:
The inheritance pattern seen in Smurfs' color where all the offspring are blue suggests that the blue coloration is dominant over white, similar to Mendel's experiments where all the F1 generation had violet flowers. This displays a Mendelian pattern of inheritance.
As for Smurfs' foot size, the presence of both big-footed and small-footed offspring indicates incomplete dominance or a codominance pattern, since the offspring display traits from both parents without blending. If this case were like Mendel's, it would be expected that the big-footed trait, assuming it's dominant, would be expressed in all F1 offspring if no other factors were involved. However, the presence of both phenotypes in the children suggests a more complex pattern of inheritance, possibly involving multiple genes.
The genotype of the big-footed, white Smurf could be determined by the phenotypes of the offspring. Assuming big feet are dominant and represented by 'B' and white coloration is recessive and represented by 'b,' the big-footed white Smurf could have the genotype 'Bb' if we assume the blue smurf carried a recessive allele for foot size ('bb'). However, since the inheritance pattern for foot size is not clear, the genotype involving foot size is a prediction rather than a certainty without more information.