Calculadora de Probabilidade de 3 Eventos Independentes
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P(A∩B∩C) = P(A)·P(B)·P(C) (independentes)
About this calculator
The Probability of 3 Independent Events Calculator computes the probability of three events A, B, and C occurring simultaneously, assuming they are independent. The formula used is P(A∩B∩C) = P(A) × P(B) × P(C), where each individual probability must be between 0 and 1. This tool is useful for situations where one event does not affect the others, such as dice rolls or coin flips.
To use the calculator, enter the probabilities of each event in the corresponding fields. The result is displayed automatically, showing the joint probability. For example, if P(A)=0.5, P(B)=0.3, and P(C)=0.2, the probability of all occurring is 0.03 (3%). The tool also validates that the values are within the correct range, displaying an error message otherwise.
When to use? In risk analysis, gambling, weather forecasting, or any scenario where independent events need to be combined. For instance, calculating the chance of three independent machines failing simultaneously, or the probability of correctly predicting three outcomes in a sequence of independent sports events.
Cautions: The formula is only valid for independent events. If there is dependence between them, the result will be incorrect. Also, ensure the individual probabilities are in decimal form (0 to 1), not percentage (0% to 100%). Always verify that independence is a reasonable assumption for your problem.
Frequently asked questions
What does independent events mean?
Independent events are those where the occurrence of one does not affect the probability of the other. For example, flipping a coin twice: the result of the first flip does not influence the second.
Can I use percentages instead of decimals?
No, the calculator expects decimal values between 0 and 1. If you have 50%, enter 0.5. The result will be in decimal; multiply by 100 to get the percentage.
What if the events are not independent?
In that case, the formula P(A)×P(B)×P(C) is not valid. You need to use conditional probabilities, such as P(A∩B∩C) = P(A) × P(B|A) × P(C|A∩B).
What is the difference between this calculator and the 2-event one?
This calculator handles three simultaneous events, while the 2-event one considers only two. The logic is the same, but with more events the joint probability tends to be smaller.