The Chain Rule for Matrix Exponential Functions
Jay A. Wood · College Mathematics Journal · 2004
Generalization. Suppose we have a game in which a player choosing k of n num-bers purchases r tickets, selecting numbers at random. For i = 1 to r, let Ai be the event “i th ticket matches j out of n numbers. ” Let the approximate probability P(A1 ∪ A2 ∪ · · · ∪ Ar) ≈∑ri=1 P(Ai) be expressed as s: 1, and let the exact proba-bility for P(A1 ∪ A2 ∪ · · · ∪ Ar) using inclusion/exclusion be expressed as t: 1, where s and t are rounded to the nearest integer. Then t − s = 0 or t − s = 1.