The problem of the 100 prisoners: The numbers of 100 prisoners are randomly distributed in 100 drawers (one number per drawer). Every prisoner is allowed to open 50 drawers If he finds his own number, he will be pardoned.

Choosing randomly 50 drawers,
the changes to find your own number is 50 %.

In this way, the probability, that all prisoners are pardoned, is
    (0,5)¹⁰⁰ ≈ 0,0000000000000000000000000000008.


But there is a strategy, that all prisoners are pardoned,
with probability ≈ 31 %.