99.97% Chance Librarians do not generate Unbreaking III trades in 1st Tier

I cycled through trades with villagers in a naturally generated Taiga village by breaking and placing lecterns in rooms with villagers (usually just one) during working hours, only placing a new lectern if the villager had lost their profession.

I was cycling through trades specifically to get Mending, Silk Touch, Sharpness V, Protection IV, Thorns III, and Unbreaking III. According to my statistics, I mined 1522 lecterns during my attempts to achieve all of the above enchantments.

I also got unbreaking I and unbreaking II 11 times during those 1522 attempts, and although I know that I did see every one of the 37 kinds of enchantments show up at some point, I did not keep a tally of every enchantment that came up to make sure that every level of every other enchantment occurred.

Probability calculation: assuming that a librarian has a 2/3 chance of having a 1st tier enchanted book trade, and that enchantment is chosen randomly from the 37 different available enchantments before choosing an enchantment level, and then the level of enchantment is selected randomly, there is a 2/333 probability of Unbreaking III with each trial. Assuming that each trial is an independent Bernoulli trial the p-value of no Unbreaking III after 1522 trials is P=0.00010. Basically, it is very unlikely that this outcome is random chance. 

Now I may have made mistakes in some of these trials (placing a second lectern or not quite waiting long enough for the trade to refresh), so assuming that the trade didn't refresh 10% of the 1522 times a lectern was mined, results in P=0.00026.

Tested in 20w06a in Vanilla Single-Player Survival on seed 7274739946809143114 at various locations near the taiga village at coordinates -1533 1737, with various taiga and plains villagers.