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A probability distribution describes how the probabilities are distributed over the values of a random variable. For discrete random variables, it lists each possible value and its corresponding probability, ensuring that the sum of all probabilities equals 1. Understanding this concept is crucial for determining any missing probabilities in a given distribution.

In a valid probability distribution, the sum of all probabilities must equal 1. This principle is essential for solving problems involving missing probabilities, as it allows us to set up an equation where the unknown probability can be calculated by subtracting the sum of known probabilities from 1.

Complementary events are pairs of outcomes in a probability space that cover all possible outcomes. In the context of probability distributions, if we know the probabilities of certain outcomes, we can find the probability of the missing outcome by recognizing that it is the complement of the sum of the known probabilities. This concept aids in efficiently determining missing values.