OR Probability Calculator
Enter P(A) and P(B). Choose whether events are independent or supply P(A ∩ B) to compute P(A ∪ B) and related measures.
P(A ∩ B): 0.1200
P(A ∪ B): 0.5800
P(A | B): 0.3000
P(B | A): 0.4000
How to Use This Calculator
- Provide P(A) and P(B) as probabilities between 0 and 1.
- Select whether events are independent or specify P(A ∩ B) directly.
- Review P(A ∪ B) along with conditional probabilities.
- Apply results to probability problems involving unions and overlaps.
Formula
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Independent events: P(A ∩ B) = P(A) × P(B)
Conditional probabilities: P(A | B) = P(A ∩ B) / P(B), P(B | A) = P(A ∩ B) / P(A)
Full Description
The union probability reflects the chance that at least one of two events occurs. When independence is assumed, the overlapping probability follows directly from marginal probabilities; otherwise, the joint probability must be specified or estimated.
Frequently Asked Questions
Can P(A ∪ B) exceed 1?
No. The calculator warns when inputs would yield a union probability greater than 1.
Do I have to assume independence?
No. Choose “custom” to provide a known or estimated joint probability.
How do I interpret conditional probabilities?
P(A | B) indicates the chance of A given B has occurred, useful for updating beliefs and solving Bayes-style problems.
Can I input percentages?
Enter probabilities as decimals (e.g., 0.6). The output is also decimal, easily converted to percentages.