One of the Bernoulli Trial assumptions states that for each trial, there can only be two outcomes: success or failure. This is true for both binomial and geometric settings. Statistically, partial "successes" or "failures" are excluded from the results. This keeps the analysis simple and straightforward.
Each trial is an independent event. The results from one trial do not affect in any way the results of any other trial. This is true for geometric settings as well as binomial ones. This concept is another Bernoulli Trial assumption.
The third condition of the Bernoulli Trial assumption states that for each trial, the probability of success is the same. This is true for geometric as well as binomial settings. Similar to the condition that the results from one trial do not affect the others, this rule states that no one trial has any more significance than any of the others, so it cannot have a greater influence on the result.
In a binomial setting, there are two variables. One is the probability of success, and the second is number of observations made. Mathematically, these are denoted by the variables p and n. The results of a binomial setting define the number of successes based on the number of attempts. The answer, x, can be a whole number anywhere from 0 to n. In a geometric setting, the answer, x, is based on the number of trials necessary to generate the first successful trial. There is only one variable in this case, p, the probability that the first success will occur after n trials. The value of x can be any number, from 1 to infinity.