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Whether it be probability, statistics, Data Science, Machine Learning, Deep Learning, or any other likewise field, having the knowledge of the distribution of data is a must or crucial, because it helps in dealing with data.

Since both the distributions (Binomial & Bernoulli) are very confusing at first for most people, they do not try to explore & understand them. Also, one more factor is that, at most of the sources of the content, no real-life examples are given to make the explanation more realistic. That’s why this blog aims to explain the difference between the two distributions with real-life examples.

Now, that being said, let’s proceed by explaining Bernoulli Distribution first.

**This distribution deals with the data which only has 1 trial & only 2 possible outcomes. Anything other than that will not fall under the Bernoulli Distribution category.**

Although anyone can use any symbol to represent the distribution for the sake of simplification, it is been represented as:

In the above image, “p” represents the probability of the event to occur; For example, the probability of getting heads in a coin toss.

For the real-life example, let’s consider the situation of passing or failing an exam. Let’s assume the probability to pass the exam is 95%, therefore the probability to fail will be 5%.

In this case, if the event to pass the exam is considered, then the Bernoulli event will contain the probability of passing the exam. Similarly, it goes for failing the exam.

**It is the collection of Bernoulli trials for the same event, i.e., it contains more than 1 Bernoulli event for the same scenario for which the Bernoulli trial is calculated.**

It can be represented using two things:

In the image above, “n” corresponds to the number of Bernoulli trials, & “p” corresponds to the probability of the event in each trial.

When there is a requirement to calculate the likelihood of the occurrence of some event a specific number of times out of a fixed number of times, the formula listed below is used.

In the above equation:

Considering the same example of the Bernoulli Distribution, let’s create Binomial Distribution from that example.

Considering 95% & 5% for passing & failing an exam for a student respectively. If we want to calculate the probability of a student to pass exactly 5 exams out of 5 exams in which it appeared, using the above probability formula it can be easily calculated.

The number of ways to select 5 out of 5 is 1, so the first term of the formula becomes 1, now we have:

Therefore, there is approximately a 77.4 % chance, that the student passes all of the 5 exams.

This is all to explain the difference between the Bernoulli & Binomial Distribution with real-life examples.

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