The probability that an event will not happen is the complement of the probability that the event will happen. If the probability of event $E$ happening is $P(E)$, then the probability that event $E$ will not happen is given by:

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

Given $P(E) = \frac{22}{31}$, the probability that the event will not happen is:

$P(\text{not } E) = 1 - \frac{22}{31}$

We subtract the fractions:

$P(\text{not } E) = \frac{31}{31} - \frac{22}{31} = \frac{31 - 22}{31} = \frac{9}{31}$

Thus, the probability that the event will not happen is:

$\boxed{\frac{9}{31}}$

Would you like more details or further clarifications?

Here are 5 related questions for practice:

1. If $P(E) = \frac{5}{8}$, what is $P(\text{not } E)$?
2. If the probability of an event not happening is $\frac{7}{15}$, what is the probability that it will happen?
3. If an event is certain to happen, what is the probability that it will not happen?
4. If the probability of an event happening is $0.6$, what is the probability that it will not happen?
5. What is the relationship between complementary probabilities?

Tip: The sum of the probabilities of an event happening and not happening always equals 1.