* Genetics: Hair color and eye color are both polygenic traits, meaning they're determined by multiple genes. However, some alleles (gene variants) are dominant while others are recessive.
* Auburn Hair: Auburn hair is often associated with a specific gene (MC1R), and it is recessive. This means both parents need to carry the gene for a child to express it.
* Green Eyes: Green eyes also result from a combination of genes, with less melanin than brown eyes but more than blue eyes. The genes responsible for green eyes are generally recessive to the genes for brown eyes.
* Brown Hair: Brown hair is dominant.
* Blue Eyes: Blue eyes also happen due to a recessive gene.
Because you need a rarer gene for auburn hair AND green eyes it is rarer than just needing the recessive blue eye gene when the more common brown hair is dominant.
Prevalence:
* Brown Hair, Blue Eyes: While blue eyes aren't as common as brown eyes overall, brown hair is the most common hair color. So the combination of brown hair and blue eyes occurs more frequently than auburn hair and green eyes.
* Auburn Hair, Green Eyes: Both auburn hair and green eyes are relatively uncommon traits, making their combination even rarer.
Conclusion:
Auburn hair with green eyes is the rarer combination.