Color-blindness is caused by a defective gene carried on the X chromosome. The counterpart to the X chromosome -- the Y chromosome -- does not contain a gene for color vision at all. A son always gets an X chromosome from his mother and a Y chromosome from his father; if the X chromosome has the defective color-vision gene, there will be no functioning gene on his Y chromosome to oppose it. A daughter gets an X chromosome from her mother and another from her father. In this example, although the girl inherited the same defective color-vision gene from her mother as her brother did, the X chromosome from her father contained a fully functional gene that was sufficient to produce normal color vision. So, the mother, in this case, carried the gene for color-blindness but the father did not.
