In order for a discrete random variable to be modeled as binomial, what must be true about the random process/experiment that generates the values for the random variable?

The correct answer is the random experiment must be done via a bernoulli process.

Step-by-step explanation:

Binomial distribution gives the number of successes in n independent experiments, all being a bernoulli trial. Bernoulli distribution can be considered as a particular case of binomial distribution where n = 1. Bernoulli experiment is a success-failure or boolean type experiment or the probability is equal for every value of random experiment.

Thus in order for a discrete random variable to be modeled as binomial, the process should be bernoulli with equal probabilities for every random variable.