Inclusion-Exclusion
Enumerate overlapping die events and trace the singles, pair and triple corrections that count their union exactly once.
Free theory articleEnumerate overlapping die events and trace the singles, pair and triple corrections that count their union exactly once.
Concept & interpretation
The Inclusion-Exclusion Principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as |A ∪ B| = |A| + |B| - |A ∩ B|.
Experiment
To verify this in the Inclusion-Exclusion module:
- Set the Sides control to 6.
- Set the Threshold t control to 4.
- Set the Terms control to 3.
Observe that the Single Sum is 8, Pair Sum is 4, and Triple is 1. The True Union is 5, with probability 5/6 (0.833333). If you next set Threshold t to 1 and Terms to 1, the Partial Term Sum is 11/6, which is correctly labelled as a partial sum exceeding 1, not a valid probability.