Answer
Because $ P\left( E \right)+P\left( \text{not}\ E \right)=1$, then $ P\left( \text{not}\ E \right)=1-P\left( E \right)$ and $ P\left( E \right)=1-P\left( \text{not}\ E \right)$.
Work Step by Step
We know that the sum of the probability of all possible outcomes in any situation is $1$.
Therefore,
$ P\left( E \right)+P\left( \text{not}\ E \right)=1$
And the probability that an event $ E $ will not occur is equal to $1$ minus the probability that it will occur.
Therefore,
$ P\left( \text{not}\ E \right)=1-P\left( E \right)$
Thus, the probability that an event $ E $ will occur is equal to $1$ minus the probability that it will not occur.
So,
$ P\left( E \right)=1-P\left( \text{not}\ E \right)$
