Consider the case where (left{A_{n}ight}_{n=1}^{infty}) is a sequence of independent events that all have the same probability
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Consider the case where \(\left\{A_{n}ight\}_{n=1}^{\infty}\) is a sequence of independent events that all have the same probability \(p \in(0,1)\). Prove that
\[P\left(\limsup _{n ightarrow \infty} A_{n}ight)=1,\]
and interpret this result in terms of how often the event occurs.
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