What type of distribution assigns the same probability to each possible value of the random variable?

The discrete uniform distribution is characterized by the property that it assigns the same probability to each possible value of the random variable. This means that if there are ( n ) different outcomes, each outcome has a probability of ( 1/n ). This characteristic is crucial for simulations and scenarios where all outcomes are equally likely, such as rolling a fair die or drawing a card from a well-shuffled deck.

In contrast, the binomial distribution, normal distribution, and geometric distribution do not provide equal probabilities for all outcomes. The binomial distribution deals with the number of successes in a fixed number of independent trials, where the probability of success remains constant. The normal distribution is continuous and is defined by its bell-shaped curve, where probabilities vary based on the mean and standard deviation. The geometric distribution focuses on the number of trials until the first success, which creates a different probability structure where some outcomes (especially the early successes) are more likely than others.

Thus, the definition and equality of probabilities across outcomes point to the discrete uniform distribution as the correct answer for this question.