I have two identical particles of non-zero spin in identical states (except possibly for the spin direction). One of them is spin up. What is the probability that both of them are spin up.
For fermions, that probability is zero, of course. Pauli exclusion principle.
For bosons, …
… the key insight is that you can not distinguish them. The possible wave functions are either (spin-up, spin-up) or (spin-up,spin-down)=(spin-down,spin-up). Hence, you get p=1/2. (From this, we can conclude that boys (p=1/3) are made up from 2⁄3 bosons and 1⁄3 fermions.)
There is also a quantum version of that puzzle.
For fermions, that probability is zero, of course. Pauli exclusion principle.
For bosons, …
… the key insight is that you can not distinguish them. The possible wave functions are either (spin-up, spin-up) or (spin-up,spin-down)=(spin-down,spin-up). Hence, you get p=1/2. (From this, we can conclude that boys (p=1/3) are made up from 2⁄3 bosons and 1⁄3 fermions.)