What is the fundamental principle for Probability regarding the sum of all outcomes?

In probability theory, the fundamental principle regarding the sum of all possible outcomes of a random experiment states that this sum must equal 1. This principle arises because when considering all potential outcomes, the total reflects the certainty that one of these outcomes will occur.

For example, when flipping a fair coin, there are two possible outcomes: heads or tails. If we assign a probability to each outcome, we find that the probability of heads (1/2) plus the probability of tails (1/2) equals 1. This means that it is certain that one of the outcomes will occur when the experiment is conducted.

This concept applies universally, regardless of the type of experiment, whether discrete (like rolling a die) or continuous (like measuring time). Therefore, understanding that the sum of all probabilities for an entire sample space equals 1 is crucial for accurately interpreting and applying probability in various scenarios.

This foundational aspect of probability helps in ensuring that probabilities assigned to different events are consistent and meaningful within the framework of probability theory.