Final answer:
The probability of both parents being carriers when the child is a carrier is high, assuming that they must have passed on the recessive allele. The probability of a sibling being a carrier is 50% when both parents are carriers. This is regardless of the sibling's gender or phenotypic expression.
Step-by-step explanation:
When calculating the probability of parents being carriers given that the child is a carrier of an autosomal recessive disorder, we must consider the inheritance pattern. Since the child is a carrier, it is certain that both parents contributed a recessive allele. The Hardy-Weinberg principle is not applied in this scenario because we have specific information about the child's genotype. The probability of each parent being a carrier rather depends on other factors, such as the allele frequency in the population, if unknown, we can't be certain but we can assume they are likely to be carriers because the child has one recessive allele from each.The probability of a sibling being a carrier is also influenced by the inheritance pattern.
Using a Punnett square, when both parents are carriers (heterozygous), the probability of a child being a carrier is 50%, assuming no new mutations or other unusual circumstances. This applies regardless of the sibling's gender or phenotypic expression of the disorder.It is important to note that a child born to a CF carrier and someone with two unaffected alleles would have a 0 percent probability of inheriting CF, but a 50 percent chance of being a carrier, providing an example of how parental genotypes affect the offspring's outcomes for autosomal recessive disorders like cystic fibrosis, sickle-cell anemia, Tay-Sachs disease, and phenylketonuria.