Colour blind man has one X chromosome with the gene for colour blindness which he receives from his mother. His colourblind sister has two X chromosomes each with the gene for colourblindness. She has received one of these from her father and one from her mother. Thus from this information, we can conclude that their father is colourblind and their mother has at least one X chromosome for colourblindness. Also, they have a normal brother. That means their mother has one X chromosome without colour-blindness genes. Hence mother is a carrier.
