Probability of Independent Events Not Happening/Corollary
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Theorem
Let $A$ be an event in an event space of an experiment $\EE$ whose probability space is $\struct {\Omega, \Sigma, \Pr}$.
Let $\map \Pr A = p$.
Suppose that the nature of $\EE$ is that its outcome is independent of previous trials of $\EE$.
Then the probability that $A$ does not occur during the course of $m$ trials of $\EE$ is $\paren {1 - p}^m$.
Proof
This is an instance of Probability of Independent Events Not Happening with all of $A_1, A_2, \ldots, A_m$ being instances of $A$.
The result follows directly.
$\blacksquare$