Three years ago, I put pen to paper and tried to calculate the mathematical probability of any given cat having 'pure' genes (AA), given that the only information you had on the background of the cat was what you could see from the pedigree page: that is, the only information you had was the appearance of all the parents and grandparents. I had pondered upon this question, after seeing a pedigree chart of one cat, having the same characteristics as all the parents and the grandparents.
I knew that the grandparents could possibly have a hidden recessive gene beneath the visible characteristics that were displayed (Aa). So I wondered, what was the mathematical probability that a given trait was pure (AA), if you were to witness the pedigree page of that cat and could only see the same trait in all the parents and grandparents.
Before I completed the mathematics, my instinct was that the chance of the trait being pure was 'quite high.' However, when I did the maths, I was shocked to see that the chance of a trait being pure (that is, the cat was AA homogenous) was only a mere 50%.
If you want to see the scrap paper containing my calculations, here it is:
![[Image: attachment.php?aid=4672]](https://kittycats.ws/forum/attachment.php?aid=4672)
Explanation for above scribbles:
Each of the four grandparents are heterogeneous (Aa) and so there is a one in three chance that their offspring are homogenous. (We can discount the "aa" offspring from the maths for we know that the recessive fur is not showing.) When combining these three different combinations for the two parents, 16 homogenous offspring are produced. Again, we can again discount the four "aa" results because we can see from the pedigree page that no cat has a recessive fur type. This means that there are (9*4)-4 different combinations.
I was surprised to see that, despite having a whole page of identical traits, the final cat only has mathematically a 50-50 chance of being pure in the given trait.
