Reviewed by David Chen, CFA | Expert in Statistical Analysis & Quantitative Finance
Use this advanced **Probability Calculator for Multiple Events** to instantly determine the likelihood of several independent occurrences happening simultaneously or at least once. Whether you are analyzing risk, gaming odds, or scientific data, our tool provides precise results and step-by-step logic.
Probability Calculator (Multiple Events)
Enter values above and click Calculate to see results.
Probability Calculator Multiple Events Formula
P(All) = P(A) × P(B) × P(C) …
P(At Least One) = 1 − [(1 − P(A)) × (1 − P(B)) × (1 − P(C)) …]
Source: Khan Academy – Probability Rules
Variables:
- Probability of Event (P): The likelihood of a single event occurring, expressed as a percentage (0% to 100%).
- P(All): The joint probability that every single listed event happens.
- P(At Least One): The probability that at least one of the events occurs (the complement of no events occurring).
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What is Probability Calculator Multiple Events?
A Probability Calculator for Multiple Events is a mathematical tool designed to compute the combined likelihood of several independent occurrences. In statistics, independent events are those where the outcome of one does not affect the outcome of another.
This calculator specifically solves for two critical scenarios: the “Intersection” (all events happening together) and the “Union” (the chance of at least one event happening). These calculations are vital in fields like insurance underwriting, stock market risk assessment, and engineering reliability testing.
How to Calculate Probability Multiple Events (Example)
- Convert all percentages to decimals (e.g., 50% = 0.5).
- To find the probability of All occurring: Multiply all decimals together. (0.5 × 0.4 = 0.2 or 20%).
- To find the probability of At Least One: Subtract each decimal from 1, multiply those results, then subtract the final product from 1.
- Multiply by 100 to return to a percentage format.
Frequently Asked Questions (FAQ)
What are independent events? Independent events are occurrences where the probability of one event happening is not influenced by whether the other event happened or not.
Why is my “At Least One” result so high? As you add more events, the statistical “surface area” increases, making it much more likely that at least one of those things will happen.
Can probability exceed 100%? No. Probability is strictly bound between 0 (impossible) and 100% (certain). If your sum exceeds 100%, you are likely using the wrong formula for independent events.
Does this work for dependent events? No, this calculator assumes independence. For dependent events, you must use conditional probability formulas.