# Math Help - Bonferroni's Inequality Proof

1. ## Bonferroni's Inequality Proof

Hello,

I am confused with the following question.

Suppose $E_1, E_2,..., E_n$ are events, then

$\sum_{i=1}^{n} P(E_i) - \sum_{i

The right hand side is Boole's inequality. Prove the left hand side.

I am trying to prove this using induction, but I am not sure if I am doing it correctly.
For $n=2$,
Let $E_1$ and $E_2$ be events,
then, $\sum_{i=1}^{2} P(E_i) - \sum_{i.
Thus, this holds true for $n=2$.

Am I going on the right track?
Any suggestion for the inductive step?

2. If I prove the Inclusion-Exclusion formula

$\sum_{i=1}^{n}P(E_i)-\sum_{i

how can I get the following inequality?

$\sum_{i=1}^{n} P(E_i) - \sum_{i

3. have u solved the problem?

Interested to know how to do this too