### Proof Bonferroni’s Inequality

Let be an event that occurs with probability for . Then where is the intersection of non-independent events .

### Proof by induction on n

Base case,

By additivity law and probability axiom

Inductive hypothesis

Suppose relation is true for , that is

Inductive Step

Let . Then

as required.

Advertisements

##### Comments

**One Response to “Proof Bonferroni’s Inequality”**

It looks like you are a real pro. Did you study about the subject? hrhr