Use mathematical induction to prove the following generalization of Bonferroni's Inequality: p(E1 ∩Fi. .∩⋯∩En) ≥p(E1)+p(E2)+⋯+p(Ea)-(n-1) where k1, E2, …, Ex are n events.

Use mathematical induction to prove the following generalization of Bonferroni's Inequality: $$ \begin{aligned} p\left(E_{1} \cap F_{i}\right.&\left.\cap \cdots \cap E_{n}\right) \\ & \geq p\left(E_{1}\right)+p\left(E_{2}\right)+\cdots+p\left(E_{a}\right)-(n-1) \end{aligned} $$ where $k_{1}, E_{2}, \ldots, E_{x}$ are $n$ events.

Use mathematical induction to prove the following generalization of Bonferroni's Inequality:
$$
\begin{aligned}
p\left(E_{1} \cap F_{i}\right.&\left.\cap \cdots \cap E_{n}\right) \\
& \geq p\left(E_{1}\right)+p\left(E_{2}\right)+\cdots+p\left(E_{a}\right)-(n-1)
\end{aligned}
$$
where $k_{1}, E_{2}, \ldots, E_{x}$ are $n$ events.

Use mathematical induction to prove the following generalization of Bonferroni's inequality: $$ \begin{aligned} p\left(E_{1} \cap E_{2} \cap \cdots \cap E_{n}\right) & \\ \geq & p\left(E_{1}\right)+p\left(E_{2}\right)+\cdots+p\left(E_{n}\right)-(n-1) \\ & \geq p\left(E_{1}\right)+p\left(E_{2}\right)+\cdots+p\left(E_{n}\right)-(n-1) \end{aligned} $$ where $E_{1}, E_{2}, \ldots, E_{n}$ are $n$ events.

Discrete Mathematics and its Applications

Discrete Probability

Probability Theory