Law of Total Probability

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 Aoccurring given each event Bn, multiplied by the probability of each Bn occurring, where Bnare 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.