Definition of a binomial trial

Question

I would like to give a precise definition of a binomial trial. Is the following a strict and correct definition of a binomial trial?

A binomial trial is n repetitions of the same basic trial, where

1. The basic trial has two outcomes, namely "success" with probability p and "failure" with probability 1-p.
2. The basic trials are independent of each other. In other words, p does not change during the n repetitions.

Answer 1

Thanks for reply. Is this better.

A stochastic experiment where

1. we consider n basic trials (the important thing is a fixed number).

2. the base trials are independent (i.e. the outcomes of each base trial have no influence on each other).

3. the probability of success is the same in each base trial, namely p.

is called a binomial trial.