There are so many **Data Science concepts** which are applied using the **Probability** such as **Recommender Systems**, **Decision Making Concepts**, **Analyze and predict trends**, informed decision about events, in **mathematical function** which provide the possibilities of occurrence of various possible outcome that can occur in an experiment, sampling in **Machine Learning**, **Deep Learning** frameworks like Tensorflow, Pytorch are based on the concepts of Probability.

## How it works??

In probability different type of data can be analyzed through different ways it can’t be the same always. Some ot them follows Normal distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, while some others follow Exponential distribution. Each of these distributions has different formulas associated with them using which we draw insights from the data. We identify the type of distribution by looking at their graphs. When we know the type of distribution our data follows we’ll know what mathematical model is relevant to our data.

Hypothesis testing is done to confirm if an idea right or wrong. There are basically two types hypothesis. Which are given below:

- Null Hypothesis
- Alternative Hypothesis

Null Hypothesis have no significant difference between the specified population and the Alternative Hypothesis have a significant difference.

## Bayes’ Theorem:

**Bayes’ theorem** named after the Reverend **Thomas Bayes****,** describes the probability of an **event,** based on prior knowledge of conditions that might be related to the event.^{} For example, if the risk of developing health problems is known to increase with age, Bayes’ theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole.

One of the many applications of Bayes’ theorem is **Bayesian inference,** a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different **probability interpretations****.** With **Bayesian probability** interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to **Bayesian statistics****.**

Bayes’ theorem is stated mathematically as the following equation

where is the probability of both A and B being true.

## Random Variables

Random Variables is a variable whose possible values have an associated probability

distribution. A very simple random variable equals 1 if a coin flip turns up heads and 0 if the flip turns up tails. A more complicated one might measure the number of heads observed when flipping a coin 10 times or a value picked from range(10) where each number is equally likely. The associated distribution gives the probabilities that the variable realizes each of its possible values.

## Probability in Daily Life:

Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial regulation.

[…] Importance of Probability In Data Science […]