Probability of Union of N Independent Events Calculator

Introduction

The probability of the union of n independent events is a fundamental concept in probability theory. When events are independent, the occurrence of one does not affect the probability of the others. This calculator helps you compute the combined probability of multiple independent events occurring.

Understanding the union of independent events is crucial in various fields including statistics, engineering, and finance. Whether you're analyzing risk scenarios or designing experiments, this tool provides a straightforward way to calculate probabilities.

Probability Union Formula

The probability of the union of n independent events can be calculated using the following formula:

Where:

• P(A₁ ∪ A₂ ∪ ... ∪ Aₙ) is the probability of the union of all events
• P(Aᵢ) is the probability of the i-th event occurring
• n is the number of independent events

This formula accounts for all possible combinations of the events occurring, including the case where none of the events occur.

Using the Calculator

Our calculator makes it easy to compute the probability of the union of independent events. Follow these steps:

1. Enter the number of independent events (n)
2. Input the probability for each event (between 0 and 1)
3. Click "Calculate" to get the result
4. Review the detailed result and chart visualization

The calculator provides a clear breakdown of the calculation and visual representation of the probabilities.

Worked Examples

Example 1: Two Independent Events

Suppose you have two independent events:

• Event A has a probability of 0.3
• Event B has a probability of 0.4

The probability of either A or B occurring is calculated as:

So, there's a 58% chance that either Event A or Event B will occur.

Example 2: Three Independent Events

For three independent events with probabilities 0.2, 0.3, and 0.4:

This means there's a 66.4% chance that at least one of the three events will occur.