A hypothetical breeding question

[Lord Sorril]

How would that worK? Say the 66% het's first HO mating produced 4 het offspring. By how much would you reduce the 66%?

Even though I ranked top of my class in statistical probability-I am lazy...
ChatGPT figure it out for me (note: it is using a sample size of *4* offspring so its calculations are a bit rounded).
TLDR: Reduce the 66% Het to ~50% Het
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Setup:

• First parent: 66% Het (66% chance of being heterozygous Hh and 34% chance of being not Het, meaning they are HH—homozygous dominant).
• Second parent: Homozygous recessive (hh), meaning they always pass on the h allele.

So, the first parent has a 66% chance of being Hh and a 34% chance of being HH.
Possible Offspring:

1. If the first parent is Hh (66% chance):
   
   • They can pass on either H (50% chance) or h (50% chance).
   • The second parent is hh, so they always pass on h.
   
   This gives the following possibilities:
   
   
   • Hh (heterozygous) — if the first parent passes on H (50% of the time).
   • hh (homozygous recessive) — if the first parent passes on h (50% of the time).
   
   So, when the first parent is Hh:
   
   
   • 50% chance of Hh offspring.
   • 50% chance of hh offspring.
   
   
2. If the first parent is HH (34% chance):
   
   • The first parent can only pass on H.
   • The second parent is hh, so they will always pass on h.
   
   This results in:
   
   
   • Hh (heterozygous) — 100% of the time.
   
   So, when the first parent is HH:
   
   
   • 100% chance of Hh offspring.

Expected Outcome:

• If the first parent is Hh (66% chance):
  
  • 50% of the offspring will be Hh.
  • 50% of the offspring will be hh.
  
  
• If the first parent is HH (34% chance):
  
  • 100% of the offspring will be Hh.

Observed Outcome:

You observed 4 offspring, and they were all Hh (heterozygous).
This result suggests that the first parent must have been closer to HH than Hh, since you didn't observe any hh (homozygous recessive) offspring at all.
Adjusting the Het Percentage:

Given the 100% Hh offspring observed, it suggests that the first parent was much more likely to be HH (homozygous dominant) than initially thought. If the first parent were 66% Het (Hh), you would expect a 50/50 mix of Hh and hh offspring, but you saw only Hh offspring.
This means the 66% chance of being Hh should be lowered to explain the outcome of all Hh offspring. Based on the observation of all Hh offspring, the first parent likely had more of a 50/50 chance between being HH or Hh, so the 66% Het should be adjusted to something closer to 50% Het.

Conclusion:
The 66% Het should be reduced to around 50% Het to explain the observation of 100% Hh offspring, as this would make it more likely for the first parent to be HH

[Homebody]

Thank you for this thoughtful response. I'm gonna have to let this bounce around in the old noodle a bit.