OR Probability
Calculate P(A∪B)=P(A)+P(B)−P(A∩B) for independent or mutually exclusive events. Free OR probability calculator with formula breakdown and interactive charts.
About This Calculator
The OR Probability Calculator helps you find the probability of at least one of two events (A or B) occurring. Whether you are studying probability theory, working on statistics homework, or analyzing real-world scenarios, this tool computes P(A∪B) and related probabilities instantly.
The core formula is P(A∪B) = P(A) + P(B) − P(A∩B). For independent events, the intersection probability is P(A∩B) = P(A) × P(B). For mutually exclusive events that cannot happen simultaneously, P(A∩B) = 0, so P(A∪B) = P(A) + P(B).
Our calculator also computes the probability of exactly one event occurring (P(A) + P(B) − 2×P(A∩B)) and the probability of neither event occurring (1 − P(A∪B)). Results are displayed as percentages with interactive bar and pie charts for easy comparison.
Regional Notes
- India (IN): Probability concepts are taught in CBSE and state board Class 10-12 mathematics curriculum under the probability chapter.
- United States (US): OR probability is covered in high school statistics and AP Statistics courses, often applied to real-world data analysis.
- United Kingdom (UK): Covered in GCSE and A-Level Mathematics and Further Mathematics, particularly in the statistics modules.
Frequently Asked Questions
How do I calculate the probability of A or B?
The probability of A or B is P(A∪B) = P(A) + P(B) − P(A∩B). For independent events P(A∩B) = P(A) × P(B). For mutually exclusive events P(A∩B) = 0, so P(A∪B) = P(A) + P(B).
What is the difference between OR and AND probability?
OR probability P(A∪B) measures the chance of at least one event occurring. AND probability P(A∩B) measures the chance of both events occurring together. The OR probability includes the AND case.
How do I calculate OR probability for independent events?
For independent events, P(A∩B) = P(A) × P(B). So P(A∪B) = P(A) + P(B) − P(A) × P(B). For example, with P(A) = 50% and P(B) = 30%, P(A∪B) = 0.5 + 0.3 − (0.5×0.3) = 0.65 = 65%.
What happens when events are mutually exclusive?
Mutually exclusive events cannot happen at the same time, so P(A∩B) = 0. The OR probability simplifies to P(A∪B) = P(A) + P(B). For example, the probability of rolling a 3 or a 5 on a fair die is 1/6 + 1/6 = 1/3.
What is the probability of neither event A nor B occurring?
The probability of neither event is P(neither) = 1 − P(A∪B). Using the complement rule, if P(A∪B) = 65%, then the probability of neither event happening is 100% − 65% = 35%.
Can probability values be negative or exceed 100%?
No, valid probabilities always range from 0% to 100%. Our calculator validates inputs and clamps results to this range.
Is this OR probability calculator free to use?
Yes, it is completely free to use with no registration required. You can share results via URL.