Complementary event

Let $E$ be an event in a sample space $S$. The probability of event $\bar{E}$, or the complement of $E$ in $S$ is the sum of the probabilities of the outcomes not in $E$: $$ \boxed{ p(\bar E) = 1 - p(E) } $$

title: Example
We flip a fair coin $10$ times, what is the probability that heads comes up at least once?
 
Let $E$ be the event that heads comes up at least once of the $10$ flips.
Let $\bar E$ be the event that each of the $10$ times, tails comes up.
 
$$
	\begin{aligned}
		p(E) &= 1 - p(\bar E) \\
		&= 1 - \frac{1}{2^{10}} \\
		&= 1 - \frac{1}{1024} \\
		&= \frac{1023}{1024}
	\end{aligned}
$$