Information about the binomial probability formula
Before anything else, it is necessary for us to understand what binomial probability is itself. See, when a binomial experiment is carried out, it tends to give out two mutually exclusives results, which are typically referred to as success and failure. In cases where the probability of success is denoted by p, the probability of failure is denoted by 1p. The binomial probabilities and the binomial table are deduced from the Bernoulli trial and when computing these, it is vital that three varying factors are to be calculated and multiplied. These factors are:

The number of ways in which r successes can be chosen

The basic probability of success denoted by p that is raised to the power r

The basic probability of failure denoted by q that is raised to the power (n – r)
Now, getting back to the binomial probability formula, there aren’t many different binomial probability formulas for you to worry about, as there is just one which is represented by:
Here in, n represents the number of trials, k represents the number of successes, p equals the probability of success in one trial, nk stands for the number of failures, and q equals 1p which equals the probability of failure in a single trial.
A few binomial probability examples
Here are a few binomial probability examples that would help you in understanding how to calculate binomial probability as well as work on binomial probabilities table.
For our first example, let us consider that you are to take a multiple choice test in which ten questions are given. Now, if every single question in the test has four choices and you are to take a guess on each question, what is the probability that you would get a full 7 questions correct? The information that we have in this question is this:
n = 10
k = 7
n – k = 3
p = 0.25
q = 0.75
If we are to apply the basic formula for calculating binomial probability, it would become:
What you should know about binomial probability distribution
Experiments that fulfill three conditions are said to have a binomial probability distribution. The conditions are:

The number of trials is fixed

All of the trials made are independent

The outcomes of such an experiment are classified either as failure or success. The probability of success should also be fixed.
Binomial Probability Video Lesson
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