What key property must the probabilities in a discrete probability distribution satisfy?

What key property must the probabilities in a discrete probability distribution satisfy?

• A. They must be less than 1
• B. They must be equal to 0
• C. They must sum to 1
• D. They must exceed 1

Answer: (C)

In a discrete probability distribution, a crucial requirement is that the sum of the probabilities of all possible outcomes must equal 1. This reflects the principle that one of the outcomes must occur. Each individual probability within the distribution can range from 0 to 1, inclusive, but when added together, they must total exactly 1. This ensures that the model accurately represents a complete set of outcomes for a particular random experiment. The option mentioning that probabilities should be less than 1 does not encompass the necessity for their total to equal 1. Stating that probabilities must be equal to 0 suggests that no outcomes have a chance of occurring, which contradicts the nature of probability distributions. Likewise, asserting that probabilities must exceed 1 is fundamentally incorrect, as probabilities cannot go beyond 1 in any proper distribution.

In a discrete probability distribution, a crucial requirement is that the sum of the probabilities of all possible outcomes must equal 1. This reflects the principle that one of the outcomes must occur. Each individual probability within the distribution can range from 0 to 1, inclusive, but when added together, they must total exactly 1. This ensures that the model accurately represents a complete set of outcomes for a particular random experiment.

The option mentioning that probabilities should be less than 1 does not encompass the necessity for their total to equal 1. Stating that probabilities must be equal to 0 suggests that no outcomes have a chance of occurring, which contradicts the nature of probability distributions. Likewise, asserting that probabilities must exceed 1 is fundamentally incorrect, as probabilities cannot go beyond 1 in any proper distribution.