Final answer:
In a scenario where x is an indiscriminate choice between a, b, or c (assuming equal likelihood and no additional context), X would follow a uniform distribution, with each outcome having a 1/3 probability. Whether choices are made with or without replacement influences the computation of probabilities. Without replacement, probabilities change as choices are made.
Step-by-step explanation:
When determining the probability model of making an indiscriminate choice between three options (a, b, or c), we consider that these choices are equally likely. The random variable X here represents the outcome of the choice.
The values X may take on are a, b, and c, each representing the distinct sites that could be chosen.
Since there are three outcomes and we assume each is equally likely, X follows a uniform distribution with each outcome having a probability of 1/3.
If the context involves choosing objects like athletes and the question asks if the choosing is done with or without replacement, it changes the way probabilities are computed. If it's with replacement, every choice is independent. Without replacement, the probabilities change as choices are made.