# Probability theory: Binomial distribution

This is part of the course “Probability Theory and Statistics for Programmers”.

**The binomial distribution** is the distribution of the number of successes in a sequence of n repeated Bernoulli trials. Repeated Bernoulli trials mean that all trials are independent and each result have two possible outcomes. Random variable X represents the number of successes in n trials. Now we can construct the formula.

If you follow the series up to this point you can mention that this formula was explained in the “Repetitive experiments” part.

Let’s take a look at the classic example. Imagine that you tossing coin 20 times. What the probability that you will have exactly 6 tails?

As you can see from chart probability that you have 6 tails is equal to the probability that you will have 6 heads. This is because you have mirroring probabilities.

Let’s take a look at the characteristics of the binomial distribution. The mean and the variance:

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