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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?
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
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