Q: meanwhile if persons A and B have the same birthday, and persons C and D have a different same birthday, then that's 2 coincidences. but say persons A, B, and C have the same birthday. are there 2 coincidences in this situation, or 3?
A: i'm trying to figure out just what we normally mean when we say 'coincidence'. it seems like, for compounding coincidences, it seems like the results have to be revealed separately. if you select 3 random numbers at the same time, and they are all the same number, that seems like 1 coincidence. however, if you select the 3 numbers one at a time, and they all turn out the same, then that would feel like 2 coincidences, because effectively your were surprised twice