Final answer:
The probability that a couple will have a son with blue eyes and freckles is 6.25%, assuming they have the correct genotypes to produce such an offspring. This calculation is based on the inheritance of the recessive alleles needed for blue eyes and freckles, along with the statistical probability of having a male child.
Step-by-step explanation:
The probability that a couple will have a son with blue eyes and freckles depends on the genetic makeup of the parents. The allele for brown eyes (B) is dominant to blue eyes (b), and since freckles are recessive, we'd represent the freckle allele as 'f'. If we assume the parents' genotypes allow for the possibility of blue-eyed, freckled offspring, we can calculate the probability.
To have blue eyes, the son must inherit a 'b' allele from each parent (bb), and to have freckles, he must inherit a 'f' allele from each parent (ff). If one parent has brown eyes and does not carry the blue eye allele, and the other parent is heterozygous for it (Bb), there is a 50% chance for a child to inherit a b allele from the heterozygous parent. The chance of having a son specifically is 50%, as sex determination is typically 50/50 between male and female offspring. Combining these probabilities, we get (50% for a b allele) x (50% for a son) = 25% chance for a son with blue eyes. If both parents can pass on the freckle trait (being heterozygous or homozygous recessive), there is a 25% chance for the child to be homozygous recessive for freckles (ff).
Combining all these probabilities, for a child to be a son with both blue eyes and freckles, we must multiply the probabilities: (25% for blue eyes and a son) x (25% for freckles) = 6.25% chance.