1. The problem involves understanding the probabilities of an event $X$ and its complement $\text{not } X$. 2. By definition, the probability of an event $X$ is denoted as $P(X)$, and the probability of the complement event $\text{not } X$ is $P(\text{not } X)$. 3. The key rule is that the sum of the probabilities of an event and its complement is always 1: $$P(X) + P(\text{not } X) = 1$$ 4. From this, we can express one probability in terms of the other: $$P(\text{not } X) = 1 - P(X)$$ and $$P(X) = 1 - P(\text{not } X)$$ 5. The problem shows a table with outcomes 1 to 10 and asks to fill in $P(X)$ and $P(\text{not } X)$, which are complementary probabilities. 6. Therefore, if you know $P(X)$, you can find $P(\text{not } X)$ by subtracting $P(X)$ from 1, and vice versa. 7. The expression $1 - P(\text{not } X)$ is exactly equal to $P(X)$, which is the probability of event $X$ occurring. Final answers: $$P(X) = 1 - P(\text{not } X)$$ $$P(\text{not } X) = 1 - P(X)$$