# Mutually exclusive events problems with answers

Recent questions in Mutually Exclusive Events
beatricalwu 2022-07-21

### Let $\mathcal{A}$=event space. Assume that $\left\{{A}_{n}\right\}$ is a monotone nondecreasing sequence of events in A$\mathcal{A}$. Let $\left\{{A}_{n}\right\}$ be a sequence of sets defined as follows:Prove that $\left\{{B}_{n}\right\}$ is a sequence of mutually exclusive events in $\mathcal{A}$. Justify each line of proof.I know that what I need to show here is ${B}_{i}\cap {B}_{j}=\mathrm{\varnothing }$ for any $i. I've divided it to be proof by cases where case $1$ is and case $2$ is $i\in \left\{2,3,4,\dots \right\}$ and $j\in \left\{2,3,4,\dots \right\}$ where $i so that and where $i\in \left\{2,3,4\dots \right\}$ and $j\in \left\{i+1,i+2,\dots \right\}$.

Lorena Lester 2022-07-20

### $A\cup B$ can be expressed as the union of two mutual exclusive events in the following way:$A\cup B=A\cup \left(B-AB\right)$Express $A\cup B\cup C$ in a similar way.

Paxton Hoffman 2022-07-20