Boole’s Inequality
Boole’s Inequality The Boole’s Inequality Theorem states that "the probability of several events occuring is less than or equal to the sum of the probabilities …
Probability Theory
Bonferroni Inequality
Bonferroni’s Inequality For $n$ events $A_1,A_2,\cdots, A_n$ $$ \begin{equation}\label{bof} P\big(\cap_{i=1}^n A_i\big)\geq \sum_{i=1}^n P(A_i) -(n-1). \end{equation} $$ Proof For $n =2$, $$ \begin{equation*} P(A_1\cup A_2)= P(A_1)+P(A_2) …
