A popular music festival with a fixed number of available tickets uses a system (algorithm?) that randomly picks from a group of registered individuals who is able to purchase a ticket. The group of registered individuals is considerably larger than the number of available tickets. Nothing confusing so far.
However, the festival organization provides the possibility for registered individuals to become part of a group (up to 20 individuals). The idea is that the system either picks everybody or nobody from a group. The festival organization claims that the probability of being picked by the system is equal for individuals and for groups. I wonder whether this is possible or not?
It is possible if groups are counted as an individual. So if the system forms a list:
person1, person2, ..., personN, group1, group2, ..., groupMand then chooses randomly from the list until all the tickets are gone. If the number of available tickets is way larger than 20, the probability to be picked either as an individual or a group member are practically the same.