>>11984064,b] ? [0,1] P([a,b]) = b – a
if the set [a,b] is a subset of [0,1], then the probability of [a,b] is b – a.
The direct consequence of this is that every single possibility is a 0-probability outcome:
?? ? ?, P({?}) = P([?,?]) = ? – ? = 0
for all sets ? that are a member of the sample space, the probability is ?, which equals the probability of the set [?,?], which equals ? – ?, which equals 0
What this example shows is that a 0-probability event is not an event that never happens, because in the case where the sample space cannot be defined it is possible for a 0-probability event to occur, because all events are p=0 and yet something must occur.
