Recent questions in Mutually Exclusive Events

Mutually Exclusive Events
Answered

beatricalwu
2022-07-21

${B}_{1}={A}_{1};{B}_{i}={A}_{i}-{A}_{i-1}\text{}\text{for}\text{}i\in \{2,3,4,\dots \}$

Prove that $\{{B}_{n}\}$ 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 $i<j$. I've divided it to be proof by cases where case $1$ is $i=1\text{}\text{and}\text{}j\in \{2,3,4,\dots \}$ and case $2$ is $i\in \{2,3,4,\dots \}$ and $j\in \{2,3,4,\dots \}$ where $i<j$ so that ${B}_{i}={A}_{i}-{A}_{i-1}\text{}\text{and}\text{}{B}_{j}={A}_{j}-{A}_{j-1}$ and ${B}_{i}={A}_{i}-{A}_{i-1}\text{}\text{and}\text{}{B}_{j}={A}_{j}-{A}_{j-1}$ where $i\in \{2,3,4\dots \}$ and $j\in \{i+1,i+2,\dots \}$.

Mutually Exclusive Events
Answered

Lorena Lester
2022-07-20

$A\cup B=A\cup (B-AB)$

Express $A\cup B\cup C$ in a similar way.

Mutually Exclusive Events
Answered

Paxton Hoffman
2022-07-20