The theory of probability is constantly present in our lives. We ignore it, but every event has one or another chance. Taking into account the vast number of possible scenarios, we must determine the most probable and the least likely of them. It is most convenient to analyze such data. One of the easiest how to find the probability is the binomial probability.

**What is Binomial Probability?**

Binomial distribution – is the number of "successes" in a sequence of independent random experiments. They show that the probability of "success" in each of them is equal to a specific value. The mathematical expectation of the binomial distribution is calculated according to the same scheme.

We take the value of a random variable, multiply it by the probability of a positive outcome, and then summarize the obtained data for all variables.

It is very convenient to present binomial probability questions, especially if you wish to find answers. So, the difference between the mathematical expectations of different values is better perceived.

**Where and When to Use Binomial Distribution?**

Many people even have no idea that binomial probability is an essential part of our life. And the statement that only mathematicians need binomial probability is incorrect.

So let's give some examples that can be answered using the binomial probability distribution.

**Pharmaceutical Quality Control**

The practical use of the binomial distribution may be quality control of a batch of a pharmacological drug. Here it is required to count the number of products that do not meet the requirements. All causes affecting the drug quality are equally probable and independent.

A complete quality check is impossible in this situation since the product that has passed the test is not subject to further use. Therefore, a certain number of product samples is randomly selected from a batch for control. These samples are comprehensively checked, and the number of defective products is recorded.

**Use for Hospitals**

The hospital manager wants to distribute the number of staff on different weekdays correctly. He knows the total number of patients admitted to the emergency department due to alcohol poisoning over a given period.

The hospital manager can analyze the distribution of the number of patients for each day of the week. He will likely have more cases like this on the weekends and will need more staff.

This can be used for other businesses as well. They can use binomial distributions to calculate demand changes and plan accordingly. To make your life easier and observe statistics.

**Use for Students**

If we talk about the benefits of probability theory for students, it will also be very significant. After all, probability theory is needed only by students of mathematics who must study it.

This knowledge will also be necessary for students of other specialties because they develop logic and critical thinking. But not all students immediately manage to understand mathematics. It is not a problem because many services and applications can help them.

Therefore, a student who wants to study mathematics should download a specific application or choose any service for learning mathematics and start from scratch. In this way, studying mathematics will be a pleasure.

**Properties Of The Binomial Distribution**

For a random variable to be considered as obeying the binomial distribution, it must meet the following properties:

● Only two outcomes are possible in each trial, experiment, or test.

● The probability of success must be constant.

● The failure probability must also be constant.

● The result obtained in each experiment does not depend on the previous one. Therefore, what happens in each experiment does not affect subsequent ones.

● The events are mutually exclusive, meaning they cannot co-occur.

● All events are exhaustive, meaning at least one of the two must occur. If you're not a man, you're a woman, and if you flip a coin, if it doesn't come up heads, then it's tails.

**What is Binomial Probability Based On?**

Binomial distributions form when we iterate over a set of events. Each event in the group has two possible outcomes. The binomial distribution pertains to these results.

In statistics, one of the areas of application of the theory of probability, there are many examples where the data for analysis is not given explicitly. That is, not in numbers, but in the form of division according to characteristics, for example, gender.

It is required to convert the initial data into a numerical format to apply the mathematical apparatus to such data and draw some conclusions from the results obtained. Thus, we receive statistical data that can be subjected to research using mathematical methods and quickly get the information we need.

**Conclusion**

Many events in real life can be explained by a binomial probability distribution, allowing us to calculate whether events happened due to random chance or not and test our hypothesis. This can be explored within a small private or larger company such as a pharmaceutical company, a hospital, or a large web service.

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