| MadSci Network: Genetics |
Red hair and green eyes are both autosomal (not linked to sex) recessive traits, meaning that they appear only in people, like your wife, who have the allele (version of a gene, e.g. the gene for hair color has different alleles for different colors) for red hair on both copies of the gene. The fact that neither of her parents had red hair demonstrates this fact: each of her parents had one allele for red hair and one allele for another color (brown or black), so that while neither of them exhibited the trait, they were both carriers (her maternal grandfather was the source of her mother's one red hair allele).
Regarding your children. Since your wife has both red hair and green eyes, you know that all of your children will have at least one copy of each recessive allele. However, for them to exhibit the trait, they each need two copies of the alleles, which means you have to be carrying the alleles, too. If any of your grandparents on your side have or had red hair, then you have a chance. If not, there's still chance: I have red hair, and my wife has brown hair; none of her grandparents had red hair, but a neice and two of her nephews do have red hair; since her brother carries the allele (hence the red headed children), one of her parents has to be a carrier, so our children could have red hair.