Empirical probability distributions require which property?

Empirical probability distributions require which property?

• A. Event categories (bins) are designed so that only the most probable events are included.
• B. The sum of all empirical probabilities in a distribution can be any number.
• C. They provide a mutually exclusive, collectively exhaustive list of outcomes.
• D. Any given event can fall into one or more categories of event (bins).

Answer: (C)

Empirical probability distributions rely on partitioning the possible outcomes into categories that are mutually exclusive and collectively exhaustive. This means every outcome falls into one and only one category, and all potential outcomes are represented by some category. This structure makes the probabilities well-defined and ensures they sum to 1 across all categories. If categories overlapped, an outcome could be counted more than once; if some outcomes aren’t included in any category, the total would fail to capture all possibilities, and the distribution wouldn’t be valid. For example, when tallying outcomes of a six-sided die, the categories are the distinct results 1 through 6; each result fits into exactly one category and together they cover every possible roll, so the empirical probabilities add up to 1.

Empirical probability distributions rely on partitioning the possible outcomes into categories that are mutually exclusive and collectively exhaustive. This means every outcome falls into one and only one category, and all potential outcomes are represented by some category. This structure makes the probabilities well-defined and ensures they sum to 1 across all categories. If categories overlapped, an outcome could be counted more than once; if some outcomes aren’t included in any category, the total would fail to capture all possibilities, and the distribution wouldn’t be valid. For example, when tallying outcomes of a six-sided die, the categories are the distinct results 1 through 6; each result fits into exactly one category and together they cover every possible roll, so the empirical probabilities add up to 1.