Colour Blindness Probabilities in One Family
In a family, a man with normal colour vision marries a woman who has normal vision but whose father is red-green colour-blind. Their first child is a boy with colour blindness. They also have an unaffected daughter. The couple plans one more child and asks a counsellor about the chance that a future son will be colour-blind and the chance that a future daughter will be a carrier. The woman's mother has normal vision and no family history of colour blindness. No genetic testing is available. The counsellor explains that red-green colour blindness is X-linked recessive and that the woman must be a carrier because of her father. The couple wants probabilities, not vague reassurance, and asks why their daughter can be a carrier even though she sees colours normally.
1. Assign genotypes and calculate the probabilities for a future son and a future daughter.
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Let X^N be the normal allele and X^c the colour-blind allele. The father is X^N Y. The mother is X^N X^c, because her colour-blind father (X^c Y) must have passed X^c to her. Sons receive Y from the father and either X^N or X^c from the mother: 1/2 normal sons and 1/2 colour-blind sons. Daughters receive X^N from the father and either X^N or X^c from the mother: 1/2 X^N X^N and 1/2 X^N X^c. No daughter is colour-blind in this couple. For the next child overall, the probabilities are 1/4 normal son, 1/4 colour-blind son, 1/4 non-carrier daughter and 1/4 carrier daughter.
2. The existing daughter has normal colour vision. What is the chance that she is a carrier, and why?
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Her chance of being a carrier is 1/2. She is already known to be unaffected, but she still received one X chromosome from her mother, who is X^N X^c. The mother transmits X^c with probability 1/2 and X^N with probability 1/2. Her father, X^N Y, gave her X^N, so either maternal allele leaves her with normal vision. Thus half of such unaffected daughters are expected to be X^N X^c carriers and half X^N X^N. Without testing, the probability is 1/2, not 1 and not 1/4.
3. Why are more males than females affected by red-green colour blindness, and why is it not passed from father to son?
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Males have only one X chromosome, so a single X^c makes them colour-blind. Females have two X chromosomes and need X^c on both to be affected; with one normal allele they are usually unaffected carriers. A father gives his Y chromosome to sons, so an X-linked allele on his X chromosome cannot pass to his sons. He gives his X chromosome to daughters, so an affected father would pass X^c to all daughters, making them carriers if the mother contributes a normal X. This explains both the higher male frequency and the absence of father-to-son transmission.