In order to understand binomial discrete distribution, let us consider the following example:

What is the probability that, when a fair coin is tossed twice, it lands on heads only once?

For the preceding scenario, we would look at all the possible outcomes of the two experiments (where tossing a coin once is one experiment).

We have listed all the possible outcomes of the two coin tosses (two experiments), as follows:

Given that, there are four possible outcomes of the two experiments, of which only two outcomes satisfy the criterion that we laid out (the coin lands on heads only once out of the two experiments). The probability of the event happening is 2/4 = 1/2 = 0.5.

Mathematically, this can be represented in the following way. The pmf of a binomial random variable X is:

The following applies:

• f(x) is the probability of an event happening
• n is the number of experiments
• x is the number of times a condition has to be satisfied
• p is the probability of an event happening

If we replicate the preceding laid-out example using the formula, we obtain the following:

• n=2
• x=1
• p=1/2

This translates to f(x) being equal to 1/2.