Final answer:
The highest probability of not carrying the sickle trait occurs when neither parent has the trait, as both have the genotype AA and would only pass on normal alleles to their children.
Step-by-step explanation:
The scenario with the highest probability of not carrying the sickle trait is when neither parent has the trait. This represents a situation where both parents have a genotype of AA, meaning they do not carry the allele for sickle cell at all. Consequently, their children would also have a genotype of AA, as they would inherit one 'A' allele from each parent. Therefore, the children would not carry the sickle cell trait.
In contrast, if both parents are carriers (having one normal and one sickle trait allele, Aa), their children have a 25% chance of inheriting sickle cell disease (two sickle alleles), a 50% chance of being a carrier like the parents (one sickle allele), and only a 25% chance of being completely unaffected (two normal alleles). If only one parent is a carrier, there's a 50% chance of the child being a carrier and a 50% chance of the child not carrying the trait at all. If only the mother has the trait, it follows the same 50% possibility like any single carrier parent.