# Law of Total Probability

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**Formula:**`P(A) = ∑ P(A∣Bn)P(Bn)`

## Introduction to Law of Total Probability Calculator

The law of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It states that the total probability of an event ** A** is the sum of the probabilities of

**occurring given each event**

*A***, multiplied by the probability of each**

*Bn***occurring, where**

*Bn**Bn*are mutually exclusive and collectively exhaustive events.

## Parameter usage:

`...probabilities`

= An array representing the probabilities P(A∣Bn)P(Bn) for each n

## Output:

`total probability`

= P(A), which is the total probability of event A

## Data validation

Each individual probability must be a value between 0 and 1, and the total sum must not exceed 1.

## Practical Applications

This rule is widely used in probability and statistics, risk assessment, decision making processes, and various fields such as finance, health sciences, and engineering.

## Summary

This calculator applies the law of total probability to determine the combined likelihood of an event based on conditional probabilities and their respective probabilities of occurrence.

Tags: Probability, Total Probability, Conditional Probability