In a discrete probability distribution, the sum of all possibilities is always?

In a discrete probability distribution, the sum of all probabilities is always equal to 1.

Here are the steps to understand why:

1. A discrete probability distribution is a list of probabilities associated with each of its possible outcomes. This is often represented in the form of a probability mass function.

2. The probabilities in a discrete probability distribution represent the likelihood of an event occurring. For example, if you were to roll a fair six-sided die, the probability of rolling a 1, 2, 3, 4, 5, or 6 would each be 1/6.

3. Because these probabilities represent all possible outcomes, when you add them together, they must total 1. This is because 1 represents certainty: something will definitely happen.

4. Therefore, in a discrete probability distribution, the sum of all probabilities is always equal to 1. This is a fundamental principle of probability theory.