Final answer:
Both parents being carriers of an autosomal recessive trait results in a 25% chance that their children will be affected by the disorder and a 50% chance the children will be carriers without showing symptoms.
Step-by-step explanation:
If both parents are obligate carriers of an autosomal recessive trait, the probability that their children will be affected is 25%, and the probability of the children being carriers is 50%.
In the case of an autosomal recessive trait, both parents must carry one copy of the mutated gene and one normal gene (heterozygous), represented as Ff. According to a Punnett square modeling the cross between two carriers, there is a 1 in 4 chance (or 25%) that a child will inherit two recessive alleles (ff), thus expressing the disorder. The same Punnett square illustrates that there is a 2 in 4 chance (or 50%) that a child will inherit one normal and one recessive allele (Ff), like their parents, becoming a carrier without expressing the disease.
The remaining 1 in 4 (25%) indicates the chance of producing a child with two normal alleles (FF), who will neither be affected nor be a carrier of the trait. Therefore, each conception independently yields these probabilities.