Final answer:
In a sequence of outcomes with two mutually exclusive events - no equalization or an equalization exactly at time 2m - the sum of their probabilities must equal 1 because they cover all possible outcomes.
Step-by-step explanation:
In probability theory, specifically when dealing with sequences of outcomes, there are certain properties that define the behavior of these sequences. One important concept is the memoryless property, which describes how future probabilities are not affected by past events in certain probabilistic situations. When considering a sequence of outcomes that either can have no equalization or an equalization exactly at time 2m, these are mutual exclusive events. This means that if one occurs, the other cannot.
Given that there are only two possible outcomes at any point in the sequence—either an equalization occurs or it does not—the sum of their probabilities must equal 1. Therefore, if we denote P(No equalization) as the probability of not having an equalization up to time 2m and P(Equalization) as the probability of having an equalization exactly at time 2m, these two probabilities must sum up to 1. The statement P(No equalization) + P(Equalization) = 1 describes this relationship.