Final answer:
The most likely scenario is that the serious genetic disease is an autosomal recessive disorder because both parents, who are second cousins, are carriers of the recessive allele but do not exhibit any symptoms.
Step-by-step explanation:
If two perfectly healthy second cousin parents have two children with a serious genetic disease, the most likely scenario is that the disease is recessive. This is because autosomal recessive disorders require two copies of the recessive allele for the disease to be expressed. These parents must both be carriers of the recessive allele, which means they have one normal allele and one disease-causing allele (heterozygous). This would not affect their health because the normal allele compensates for the recessive one. However, their children could inherit a recessive allele from each parent, resulting in the expression of the disorder. The fact that the parents are second cousins might increase the likelihood of this scenario, as there could be a higher chance of both carrying the same recessive allele inherited from a common ancestor.
Considering that the children have equal chances of inheriting the disease regardless of their gender, it is not an X-linked recessive disorder. dominant disorders usually manifest with just one copy of the faulty gene, so if the disorder was dominant, one of the parents would likely show symptoms. Therefore, recessive genetic disorders, like cystic fibrosis or Tay-Sachs disease, are the most probable cause for the children's condition.