What are the odds of a librarian villager selling Mending books at tier 1?

I'm currently interested in finding a librarian villager that sells Mending enchanted books, since I have been fishing forever and it's just too slow. My logic is once I find a single Mending villager, I technically have a limitless resource of mending books, so why not give it a shot?

I have a working villager farm already, but I was wondering, what are the odds of a librarian villager spawning and being able to sell Mending books at tier 1? The wiki says the following

The enchantment is chosen randomly, with equal chance of any enchantment type occurring and equal chance to get any level of it, so higher-leveled enchantments are as likely to get as low-leveled enchantments. The price in emeralds depends on enchantment level and "treasure" status. The possible values are 5 – 19 emeralds for Lvl I, 8 – 32 for Lvl II, 11 – 45 for Lvl III, 14 – 58 for Lvl IV, and 17 – 71 for Lvl V. For "treasure" enchantments the price is doubled. Note that the cost is capped to 64, meaning that for example Lvl V books truly range from 17 - 64 emeralds with costs at the upper end of the range being more common.

Does this mean that, there being 30 total enchantment types, I have a 1/30 chance of the librarian being a Mending seller, or is the enchanting pool made out of every enchantment at every level?

For example, taking into account only Sharpness and Infinity, and Sharpness having 5 levels, is the enchantment pool 6 or is it 2 and then if Sharpness is selected, a random level is selected?

Solution 1:

First the type of enchantment is selected randomly and then after that the level of enchantment is selected randomly. This means the probability of choosing mending is 1/(number of enchantments).

In you simplified example of Sharpness and Infinity, there is 1/2 probability of choosing Sharpness. Then the level of sharpness is determined by another random roll.