Final answer:
The chances of a colorblind father and a carrier mother having a colorblind child are 50% for sons (as they will receive the Y chromosome from the father and possibly the X chromosome with the recessive allele from the mother) and 25% for daughters (if they inherit the recessive allele from both parents).
Step-by-step explanation:
Colorblindness is a sex-linked recessive trait, which means that a male only needs to inherit one allele for colorblindness to be affected, while a female needs to inherit two alleles (one from each parent) since females have two X chromosomes.
For a child to be colorblind, they must receive the recessive allele from both parents. Since the father is colorblind, he can only pass on the colorblind allele to his daughters (as he provides the Y chromosome to sons). If the mother is a carrier, there is a 50% chance she will pass the colorblind allele to her children.
Therefore, all sons born to this couple would receive the Y chromosome from the father and the X chromosome from the mother. If the mother passes on her X chromosome with the colorblind allele, the son will be colorblind. For daughters, they would receive one X chromosome with the colorblind allele from the father and they have a 50% chance of receiving a second X chromosome with the colorblind allele from the mother, which would make them colorblind.
As a result, there is a 50% chance sons will be colorblind and a 25% chance daughters will be colorblind (if they inherit the X chromosome with the colorblind allele from the mother), making the overall chance for having a colorblind child 50% for sons and 25% for daughters.