Probability of 3 Events Calculator

Probability of Three Independent Events

When you know the probabilities of three independent events $A$, $B$, and $C$, you can calculate the chance that all happen, none happen, or exactly one happens. This calculator handles those common scenarios and shows the core independent-event formulas behind the answers.

Main Formulas

$$P(A \cap B \cap C) = P(A)P(B)P(C)$$

$$P(\text{none}) = (1-P(A))(1-P(B))(1-P(C))$$

$$P(\text{at least one}) = 1 - P(\text{none})$$

For exactly one event, add the three exclusive cases: only $A$, only $B$, and only $C$.

What This Calculator Returns

• The probability all three events occur;
• The probability none of them occur;
• The probability exactly one occurs;
• The probability exactly two occur; and
• The probability at least one event occurs.

Independent Events Requirement

These formulas assume the events are independent, meaning one event happening does not change the probability of the others. If your events are dependent, you need conditional probabilities instead.

Related Tools

For two-event unions and overlaps, use the OR Probability Calculator. For broader basics, see the Probability Calculator and Conditional Probability Calculator.