Probability of 3 Events Calculator

For independent events, combine probabilities by multiplying (AND) or complementing (OR).

How the Math Works

The Probability of 3 Events Calculator uses two fundamental formulas to combine independent event probabilities. For the probability of all three events occurring simultaneously, we multiply their individual probabilities: all = A · B · C. This works because each event is independent, meaning the occurrence of one doesn't affect the others. For the probability of at least one event occurring, we use the complement rule: any = 1 - (1-A)(1-B)(1-C), which calculates the certainty of something happening by subtracting the probability that none occur from 100%.

Practical Applications

To use this calculator, first identify three independent events and determine each probability as a decimal (for example, 30% becomes 0.3). Enter these values into the calculator to instantly find both the joint probability of all events happening together and the likelihood of at least one occurring. This is particularly useful in risk assessment scenarios, such as calculating the probability of three independent system failures or determining if three independent investment opportunities will all succeed.

Day-to-Day Use

This calculator helps with everyday decision-making involving multiple risks or opportunities. For instance, when planning a trip, you might calculate the probability of both flights, hotels, and rental cars being available and affordable during your desired dates. It's also valuable for understanding combined risks in personal finance, medical decisions, or event planning where multiple independent factors could influence the outcome.

Worked example

0.5, 0.4, 0.3 → all 0.06, any 0.79.

FAQ