OR Probability Calculator
Calculate the probability of event A OR event B with union formulas and Venn diagram visualization
Calculate OR Probability P(A ∪ B)
OR Probability Results
Main Result
Component Probabilities
Formula Used
Union probability equals sum of individual probabilities minus intersection
Step-by-Step Calculation
Given probabilities:
P(A) = 0.50%
P(B) = 0.50%
For independent events:
P(A ∩ B) = P(A) × P(B) = 0.50% × 0.50% = 0.00%
Using the OR probability formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = 0.50% + 0.50% - 0.00%
P(A ∪ B) = 1.00%
Interpretation
The probability that at least one of the events A or B will occur is 1.00%. This means that in 1 out of 100 trials, you can expect either event A, event B, or both events to happen.
Quick Examples
OR Probability Rules
General Formula
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Independent Events
P(A ∩ B) = P(A) × P(B)
Mutually Exclusive
P(A ∩ B) = 0
Events cannot occur together
Event Types
Independent
One event doesn't affect the other
Mutually Exclusive
Events cannot happen simultaneously
Custom
Specify your own intersection probability
Understanding OR Probability
What is OR Probability?
OR probability, also known as union probability, calculates the likelihood that at least one of two events will occur. It answers the question: "What's the probability that event A happens, or event B happens, or both happen?"
Key Concepts:
- Union (∪): The combination of all outcomes from both events
- Intersection (∩): Outcomes that occur in both events
- Complement: The probability that neither event occurs
Common Examples
Coin Flips
Getting heads on first flip OR heads on second flip
Dice Rolls
Rolling a 1 OR rolling a 6 on a single die
Weather Events
It rains OR it snows tomorrow
Venn Diagram Interpretation
In a Venn diagram, the OR probability represents the total colored area of both circles, including their overlap. The overlap represents events that happen together, which is why we subtract it once in the formula to avoid double-counting.
Formula Breakdown:
- P(A): Probability of event A (including overlap)
- P(B): Probability of event B (including overlap)
- P(A ∩ B): Overlap probability (counted twice, so subtract once)