# Bayes Theorem and its Applications

Bayes’ theorem is one of the very important concepts that you will come across when you study the subject of probability. The theorem is named after the famous logician and mathematician, Thomas Bayes. Bayes theorem is a theorem that helps you in determining the probability of any given event which is depending on a set of events that has already happened. In mathematical language, Bayes’ theorem helps us in finding out conditional probability. Now, a question will pop into your head. What do you mean by conditional probability? As the same suggests, it has some conditions attached to it. Conditional probability is the probability of an event, provided another event related to it has already happened. In this article, we discuss the Bayes theorem and its concepts. But before that lets us learn about how probability originated.

## Origin of the Subject of Probability

You will be amazed to know about the origin of the subject of probability. One of the very first applications of probability that we know of is that a group of mathematicians based in Europe used the concepts of probability to increase their chances of winning in various games of gambling. Mathematicians and logicians like Pierre- Simon De Laplace, Abraham De Moliere, Thomas Bayes, Fisher, and so on further developed the subject of probability. Earlier, the subject was part of Mathematics, but today it is a full-fledged subject in itself.

What Do You Mean by the Bayes’ Theorem?

Bayes’ theorem, also referred to as the Bayes’ rule, is a theorem to find out the conditional probability of an event. The formula to calculate conditional probability using the Bayes’ theorem is given below:

P(X|Y) = P(X) × P(Y|X)/ P(Y)

Where, P(X|Y) is the probability of occurrence of event X, given that event Y has already occurred,

P(X) is the probability of occurrence of event X,

P(Y|X) is the probability of occurrence of event Y, given that event X has already occurred, and

P(Y) is the probability of occurrence of event Y.

## Some Important Applications of Bayes’ Theorem

• The concept of Bayes’ theorem or the Bayes’ rule is widely used in the area of finance and investment. It is used to determine the rate of risk if one lends money to borrowers. Risk evaluation can be effectively done using the Bayes’ theorem. You can also take the help of Bayes’ theorem to pick up shares and stocks while investing.
• Bayes’ theorem is also used in the field of pathology and medical tests. Statistics of how likely a person is to have any disease can be found out using this concept. It is also used to determine the accuracy of medical tests.
• Bayes’ theorem has its applications in the field of data science. Majority of the problems of the subject of data science uses probability to derive its solutions. Bayes’ theorem specifically is a tool of probability that comes to the rescue of data scientists majority of the time.
• Bayes’ theorem is also used in the development of games. Many algorithms of computer programming benefit greatly from this theorem. Computer programming languages like Python, C++, etc use Bayes’ theorem.
• Bayes’ rule is also used in the many practical life examples. Probability of an earthquake occurring provided a tsunami has already occurred, probability of a storm occurring provided a light rainfall has already occurred are some of the practical life examples of Bayes’ rule.