Given the relationship:

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

This equation states that the probability of event $E$ plus the probability of the event not $E$ (i.e., the complement of $E$) is equal to 1.

To fill in the blanks:

• $P(\text{not } E)$ equals $1 - P(E)$ because the probability of the complement of an event is $1$ minus the probability of the event itself.

• $P(E)$ equals $1 - P(\text{not } E)$ because the probability of the event is $1$ minus the probability of its complement.

Thus, the completed statement is:

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

Would you like any further explanation or details on this topic?

Here are five related questions to explore this concept further:

1. What is the probability of the complement of an event if $P(E) = 0.7$?
2. If $P(\text{not } E) = 0.4$, what is $P(E)$?
3. How would you interpret $P(E) = 0.8$ in a real-world context?
4. What is the sum of $P(E)$ and $P(\text{not } E)$ when $P(E) = 0.6$?
5. How do you calculate the probability of either event $E$ or event $F$ occurring?

Tip: The sum of the probabilities of an event and its complement is always 1. This can be a useful check to ensure your probability calculations are correct.