Let's consider a task about shooting at a target.
The probability of hitting the target in a single shot is 0.6. We want to calculate the probability of hitting the target 4 times in 10 shots.

We can't solve this task using the classic definition of probability because elementary events of this stochastic experiment have different probabilities of occurring. In addition, we are conducting not one stochastic experiment but ten, and we need to consider the results of all individual experiments.
This stochastic experiment is a Bernoulli trial: we have only two possible outcomes ( shoot and fail to shoot the target).
Shots are independent, so we have a Bernoulli process and can calculate probability using Binomial distribution.