What is the Binomial Distribution?
Binomial Distribution: A probability distribution that models the number of successes in a fixed number of independent trials, where each trial has exactly two possible outcomes and a constant probability of success.
The binomial distribution is one of the most widely used discrete probability distributions. It applies whenever you're counting how many times something "works" (a success) out of a set number of attempts , think: how many free throws go in out of 10 shots, or how many items pass quality control out of 50 tested.
We write to mean: " follows a binomial distribution with trials and probability of success ."
Think of it like flipping a weighted coin times and counting how many heads you get. Each flip is independent, there are only two outcomes (heads or tails), and the coin doesn't change between flips. That's binomial thinking.