# What is the Probability That a Female Cousin is Color Blind if the Female Person is Color Blind

Note:

To be color blind you need 2 color blind allele. So color blind allele are recessive. In females, color blinds only occur if both of the alleles are recessive.

Cousins are of course biological cousin.

Genetic similarity defined as the partial derivative of expected value of having a color blind allele of a cousin as a function of the percentage of you having color blind allele is 1/8.

I think I should add that color blind alleles are extremely rare. It's actually 5% but you can presume it's .0000001%. However, you, a female, is color blind. What's the chance that your cousin is color blind?

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More information/clarity is needed to turn this into a mathematics question... – copper.hat Jun 11 '12 at 1:39
You ignore any sex-relatedness of this particular type of color-blindness? (As I recall, the most common red-green color-blindness is on the Y chromosome, so the sex comes into these calculations.) – GEdgar Jun 11 '12 at 1:40
Yea, I'll add that. Color blind people must be male. However, the color blind thingy is in X chromosome. Y chromosome never form allele. – Jim Thio Jun 11 '12 at 1:54
You contradicted yourself. Males only have one $X$ chromosome, so they only have one allele for genes on that chromosome. Females with two "color-blind" alleles could be color-blind. – Robert Israel Jun 11 '12 at 2:04
Let me check again. Females are rarely color blind. – Jim Thio Jun 11 '12 at 3:07

Suppose that no one ever comes to Grey City, no one ever leaves, and every male is colour-blind. Then the probability that a male cousin of a colour-blind person is colour blind is $1$.