ON THE PROBABILITY OF THE OCCURRENCE OF AT LEAST m EVENTS AMONG n ARBITRARY EVENTS

The following sections are included:

• Introduction

• Generalization of Poincaré's formula; Generalization and sharpening of Boole's inequality

• Generalization of Fréchet's inequalities and related inequalities

• The p_{α1 … αi}'s in terms of the p_m(v₁, …, v_k)'s and the p[_{α1 … αi]}'s in terms of the p₁(v₁, …, v_k)'s

• A condition for existence of systems of events associated with the probabilities p₁(v₁, ⋯ , v_k).