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PaperclipPerfector  1d ago (text post)   934 thread views

Small-Scale Question Sunday for November 23, 2025

Do you have a dumb question that you're kind of embarrassed to ask in the main thread? Is there something you're just not sure about?

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I have a genetics problem I don't know if my math/analysis is right because I haven't had to do math or Punnett squares in approximately 20 years and I was always kinda shit at statistics. I nerd baited myself I guess because I've been thinking about this for a week:

My wife has blue eyes. I have brown eyes as did both my parents, but both my grandmothers had blue eyes. So I know my parents were both carriers for blue eyes. The chances of me also being a carrier is 2/3 then, so the chances of my first child having blue eyes is 1/3. Our oldest came out with blue eyes so now the chances of having a kid with blue eyes is 1/2 because that confirms I'm a carrier. But what if my oldest came out with brown eyes? What would be the chances for every subsequent child to have blue eyes if all their older siblings had brown eyes?

My initial guess was 2/3s of whatever the last probability was. So kid #2 would be 2/9, then #3 would be 4/27, but that seems to drop off way too quickly. Doesn't pass the smell test.

I thought maybe I have to evaluate the probability that I'm a carrier before bringing the wife into it. So that would mean if I had a brown eyed first born, my chances of being a carrier are the chances I had a blue eyed kid for #1 [without knowing my status yet], divided by the chances that I had a blue eyed kid for #1 [without knowing my status yet] plus the chances that I had a brown eyed kid [in the event that I'm not a carrier, which is 1/3 atm]. I reasoned this because having a brown eyed kid will lower the chances of subsequent blue eyed kids so it goes in the denominator. That way, it still maintains the possibility while making it subsequently less likely.

This would be (2/3 x 1/2)/[(2/3 x 1/2)+(1/3)] which is (1/3)/(2/3) which is 1/2, making the chances of us having a blue eyed kid for #2 now 1/4. Kids number 3 and then 4 would be 1/6 and 1/10 respectively. This seems way more reasonable, but my equations are just going on vibes here. I have no idea if its right so can any math people clue me in?

both my grandmothers had blue eyes. So I know my parents were both carriers for blue eyes

both my grandmothers had blue eyes. So I know my parents were both carriers for blue eyes.

Maybe. Kind of. There are recessive brown eyed genes. Two blue eyed parents can possibly have brown eyed children. The examples of Mendelian genetics used in high school tend to be extremely oversimplified. They really shouldn't use these examples without a huge warning that any practical application on humans may defy what you were taught. Reality tends to be very polygenic with a lot of codominance unlike the Punnett squares we learned in school. When we learned Punnett squares in middle school in the 90s, our teacher warned us this is a huge oversimplification that only works for carefully selected traits like pea plant stalk shape and not common traits in humans.

https://www.nature.com/articles/s41433-021-01749-x.pdf

I am never not awed by the things Mottezins obsess about. My own mother had blue eyes, and so did my dad. My eyes are hazel. My high school biology teacher told me to check the milkman's eyes. My high school biology teacher was an ass.

Are you sure? The prior probability for a man who is confident of "his" kid's paternity to actually be a cuckold is 2%, and the eye thing must raise it by at least a few more percentage points. I'd check, if I were you.

Hell, I didn't even have any indication to doubt my lineage (my father and I look a lot alike), but one of the reasons I got a set of 23andMe kits for me and my parents is that I wanted to be certain (the other reason is that I wanted to know how white I was; it's a Hispanic thing). Turns out, he truly is my real dad; good to know.

I am sure, yes.

Seems like the kind of thing one would want to know. Do you have other objective biological indicia to support the assumption that your mother's husband is your father?

It was always incredibly obvious that my dad was my dad. It was like those, "don't talk to me or my son ever again" memes.

This is a standard application of Bayes's theorem. The probability that you are a carrier given that you have N consecutive children with brown eyes and zero with blue eyes is 1/(2N-1 + 1) so the probability that your next child will have blue eyes is 1/(2N+2). When N = 0, this agrees with your correct statement that the probability that the first child has blue eyes will be 1/3.

Bayes's theorem says that

P(Carrier|N children with brown eyes) = P(N chlidren with brown eyes | carrier) P(carrier)/P(N children with brown eyes).

You are correct that the a priori probability that you are a carrier is 2/3. Clearly P(N children with brown eyes | carrier) = 1/2N. To compute the probability that you have N children with brown eyes unconditionally, you need to take P(N children with brown eyes | Carrier) P(Carrier) + P(N children with brown eyes | Not Carrier)P(Not Carrier) = 1/2N * 2/3 + 1 * 1/3 = 1/3 * [(2N-1 + 1)/2N-1].

Hence Bayes's theorem gives

P(Carrier|N children with brown eyes) = [1/2N * 2/3]/[1/3 * [(2N-1+1)/2N-1]] = 1/(2N-1+1).

A nice visualization of this answer:

Draw three squares of equal area 1/3, two squares representing you being a carrier and one not. Then, carve out a 1/2N-fraction of the two carrier squares and color those blue (this represents the probability that your children all have brown eyes AND you are a carrier), and take the entire non-carrier square and color it brown (this represents the probability that your children all have brown eyes AND you are not a carrier). The probability that you are a carrier is the blue area divided by the blue + brown areas, which is [2/3 * 1/2N]/[2/3 * 1/2N + 1/3] = 1/(2N-1 + 1)

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