Zach said:
You're mistaking the chance of transmission (50%) with randomness. You're not guarenteed 5/10 TH carriers if you breed 10 cows to th carriers. You could get 0/10. Unless you have some unreleased genetics info we don't know about
I'm not arguing that it is possible that you won't get a single carrier, you could get really lucky. Chances are more in the favor that you will see closer to 5 than 0 though. And it can also go the other way. You can get really unlucky (or lucky if you are looking for the increased bone, etc that comes with THC animals) and get 8 or 9 out of your 10 calves that are THC.
It is generally known and accepted based on the laws of Mendelian inheritance that 50% of the time when mating THC x THF you will get THC. This is saying that you have a 50% chance of getting THC, and you also have 50% chance of getting THF with every single mating you make. I think we've digressed from the original topic and that if you are going to breed a Monopoly daughter to Walks Alone, you really oughta test her first so you don't end up with dead calf for a reason you could have prevented.
That being said, if you are still interested in the genetics and probabilities....
"Yes it is a probability game, I will give you that, and sample size can alter what we see in real life..." If you increase the number of observations to say 50, you will see closer to 25, and again if we increase the number of matings to 500, you are going to see closer to 250. Trust me when I say that the geneticists test the statistics to confirm autosomal recessive inheritance. If you would like me to go into how it is tested I can.
Sometimes its easier to think about it in an example we all know well. If you flip a coin you have a 50% chance of getting heads and a 50% chance of getting tails. If you only do it 10 times, you aren't going to get 5 heads and 5 tails every time. You will see variation. Providing you have a fair coin, as you increase the number of times you flip your coin you are going to find you get closer and closer to 50% of the flips resulting in heads and 50% of the flips resulting in tails.
To say that a bull is a "hot carrier" and has a higher chance of producing a THC or THF calf when mated to a THF cow is completely against the laws of inheritance. He has the same chances of passing on T as he does t (see above example) no matter what!