Final answer:
The probability that offspring (III-3 and III-4's child) will have an autosomal recessive trait is 1/4, as both parents are carriers. This was determined using a Punnett square for carriers of the trait.
Step-by-step explanation:
The question pertains to the probability of offspring being affected by an autosomal recessive trait when two carriers (III-3 and III-4 from the pedigree) marry and have a child. To determine this, we would typically use a Punnett square to illustrate the potential genotypes of their offspring. Since the trait is autosomal recessive, both parents would have to be carriers, meaning they have one normal allele and one allele for the disorder. We denote carriers as Aa, where 'A' is the normal allele and 'a' is the allele for the disorder.
Using a Punnett square, we see that two carriers (Aa x Aa) can produce offspring with the following genotypes: AA (normal), Aa (carrier), Aa (carrier), and aa (affected). The probability for each genotype would be 1/4, and the probability that their child will have the disorder (aa) would thus be 1/4.
Therefore, the correct answer is:
a) 1/4 - There's a 25% chance that their first child will be affected with the trait if both parents are carriers.