Why must every value of a probability mass function be nonnegative?

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sample space for a pair of dice — probability theory Sample space for a pair of dice.

In probability theory, a probability mass function ( $f (x)$ ) serves as a numerical measure of the likelihood that a specific event will occur.12

By definition, probabilities are assigned on a scale ranging from 0 to 1. Because a negative probability has no physical or mathematical meaning in the context of measuring the likelihood of an event, the function must be nonnegative for every value of the random variable. This requirement, alongside the condition that the sum of all probabilities must equal one, ensures that the function provides a valid probability distribution for a discrete random variable.12