OR Probability Calculator

What OR Probability Means

OR probability asks for the chance that at least one of two events happens. In set notation, this is the union of events $A$ and $B$, written as $A \cup B$. It includes outcomes where only $A$ happens, only $B$ happens, and both happen together.

OR Probability Formula

The main formula is:

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

You subtract the overlap once because adding $P(A)$ and $P(B)$ counts the intersection twice.

Independent vs Mutually Exclusive Events

If the events are independent, then:

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

If the events are mutually exclusive, they cannot happen together, so:

$$P(A \cap B) = 0$$

This calculator supports both cases and also lets you enter a custom overlap when you already know $P(A \cap B)$.

What This OR Probability Calculator Returns

• $P(A \cup B)$, the chance that at least one event occurs;
• $P(A \cap B)$, the chance that both occur;
• The probability that exactly one event occurs;
• The probability that neither event occurs; and
• The complements $P(A')$ and $P(B')$.

Related Probability Tools

If you want broader probability help, check the Probability Calculator, Odds Probability Calculator, and Bayes Theorem Calculator.