why does binomial random variable require fixed number of trails?

I'm currently learning binomial random variable on Khan academy and in one of the video, Sal said that in order for a random variable to qualify as a binomial random variable, it has to meet four conditions

1) the outcome of each trail can be classified as success or failure

2) each trail is independent of each other

3) there is a fixed number of trails

4) the probability of success on each trail is constant

Could someone please explain the logic behind point 3? Why is fixed number of trail a requirement for random variable to qualify as a binomial random variable?

• This is just a description of what a binomial RV is. These are the conditions upon which the binomial probability mass function, which allows us to calculate probabilities, is built. If these conditions aren't met, we would need to use a different model to calculate the probabilities that the RV would take on particular values. Commented Apr 5, 2018 at 4:11