# Bayes Rule

Bayes’ Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in *subjectivist* or *Bayesian* approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning.

Bayes’ Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem’s central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology.

Below is the formula for Bayes’ Theorem and the values can be implemented to calculate it.

Let’s explain the formula as below:

We can solve one example to get more understanding.

A Indian soccer team acquired a new player for a new season. The team played 20 games with the results:

The new player scored in the games both when his team won or lost with the following cases:

**Question:**

Find out the probability of such event that the team wins given that the new player scores.

Let’s create table from above details:

We need to calculate below given probability before getting into conditional probability :

Now we must put values in given formula where Team wins, and player scored.

Hence, Probability of Team won, and player scored in match is

Which has probability 83.34%.

# Let’s follow technical method to solve given problem.

URL : https://stattrek.com/online-calculator/bayes-rule-calculator.aspx

steps:

- Go to link given above.
- Input values calculated by probability.
- Compute the result and check for summary report.

Here is summary report for given problem.

Hence, Probability of Team won, and player scored in match is

Which has probability 83.34%.

**Reference : ****Stattrek**, **plato.stanford.edu**