Answer:
Hayden- heterozygous dominant
Mother (Helen)- heterozygous dominant
Father (Harry)- homozygous recessive
Sister (Holly)- homozygous recessive
Explanation:
This is a genetic scenario involving a single gene coding for number of arm-like extensions in Heliodors family. According to the question, the allele for four arm extensions (A) is dominant over thr allele for two arm extensions (a). The question also states that Hayden and his mother have four arm extensions while his sister (Helen) and Father (Harry) have two arm extensions.
Firstly, it is worth it to note that Harry and Holly will be genotypically homozygous recessive (aa) because a recessive trait will only be expressed in a homozygous state, since two arm extensions is the recessive trait.
Now, since father is homozygous recessive, he will produce gametes that contains only "a" allele. If the mother were homozygous dominant (AA), no recessive offspring should be produced because all the offsprings wil phenotypically have four arm extensions. But one has two (recessive) which is the sister (Holly). This is because, although, the mother phenotypically has four, but is genotypically heterozygous dominant (Aa). Hence, it can produce A and a allele in gamete formation. Therefore, Helen has heterozygous dominant (Aa).
Lastly, Hayden also has four arm extensions, hence dominant. But since Aa genotype and aa genotype from Helen and Harry respectively, came together, no homozygous dominant offspring can be produced. This tells us that Hayden must be a heterozygous dominant.
