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  • STA256 Lecture 03

Boole's Theorem

• Let $\{C_n\}$ be an arbitrary sequence of events
• $P\left(\bigcup _{n=1}^{\mathrm{\infty }}{C}_n\right)\le \sum _{n=1}^{\mathrm{\infty }}P(C_n)$
• Because the unions could have overlap, whereas the sum doesn't account for that.