The probability of an event not occurring is given by:

$P(\text{not } E) = 1 - P(E)$

Here, the probability of event $E$ occurring is:

$P(E) = \frac{1}{7}$

So the probability of $E$ not occurring is:

$P(\text{not } E) = 1 - \frac{1}{7} = \frac{7}{7} - \frac{1}{7} = \frac{6}{7}$

Thus, the probability that $E$ will not occur is:

$\boxed{\frac{6}{7}}$

---

Would you like further clarification or examples? Here are some follow-up questions to deepen understanding:

1. How is the concept of complementary probability used in real-life scenarios?
2. What happens if $P(E)$ is equal to 0 or 1?
3. Can the probability of an event ever exceed 1? Why or why not?
4. How would this calculation change if $P(E)$ was given as a decimal or percentage?
5. Why does the sum of probabilities of an event and its complement always equal 1?

Tip: Always double-check your calculations to ensure the probabilities add up to 1 when dealing with complementary events.