Bonferroni Inequality

Bonferronis 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) …

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