In probability theory, any given event [tex]\( E \)[/tex] has a certain probability of occurring, which we can denote as [tex]\( P(E) \)[/tex]. Similarly, the probability that the event does not occur, which we denote as [tex]\( P(\text{not } E) \)[/tex], is also defined. These two probabilities, [tex]\( P(E) \)[/tex] and [tex]\( P(\text{not } E) \)[/tex], are complementary in the sense that one or the other must happen, and they together cover all possible outcomes.
The probability of an event [tex]\( E \)[/tex] occurring and the probability of the same event not occurring must sum to the total certainty of all possible outcomes for the event, which is always 1 (or 100%). In other words:
[tex]\[ P(E) + P(\text{not } E) = 1 \][/tex]
So, the sum of the probability of an event occurring and the probability of that same event not occurring is 1.
The correct answer that aligns with this fundamental principle of probability is:
C. 1
