In quantum mechanics, fermions are based on the Pauli exclusion principle. In Probability theory, possible outcomes for something are complements and the sum of all probabilities equals 1. To illustrate that similar graphs to the ones used in the set theory can be applied.
When the wave functions of fermions do not overlap, the Pauli exclusion principle is not used for them (so for example different tosses of a coin wouldn’t make the wave inference effect explained yesterday). The same ideas can be extended to the probability theory. Different outcomes can be considered as fermions or bosons (based on the situation – if they are independent or not).
UPDATE 1:
Complement is a term used in set theory. However, in probability complements exclude each other so it’s better not to use that word in probability. I used the word to link it to set theory.
UPDATE 2:
The inability to observe plays a role in probability. When a box contains invisible objects (visibility means they cannot be sensed by human senses), they cannot be picked.
The point at inf is a vital part of observation, this is also true in probability. A coin is hypothetically tossed an inf number of times and that’s how the probability has been calculated.