Overlapping Probability Calculator
Calculate the probability of overlapping events with our advanced probability tool
Event A
Event B
Probability Results
Enter probabilities to see interpretation of results.
Visualization
📊 Probability Rules Reference
Union Rule
P(A∪B) = P(A) + P(B) - P(A∩B)
For P(A)=30%, P(B)=40%, P(A∩B)=12% → P(A∪B) = 30 + 40 - 12 = 58%
Independent Events
P(A∩B) = P(A) × P(B)
For P(A)=30%, P(B)=40% → P(A∩B) = 0.3 × 0.4 = 12%
Mutually Exclusive
P(A∩B) = 0
P(A∪B) = P(A) + P(B)
Conditional Probability
P(A|B) = P(A∩B) / P(B)
If P(A∩B)=12%, P(B)=40% → P(A|B) = 12 / 40 = 30%
🌍 Real-world Probability Examples
Scenario: Disease with 2% prevalence (P(A)), test with 95% accuracy (P(B|A) = 95%, P(¬B|¬A) = 95%)
Calculation: P(A∩B) = 0.02 × 0.95 = 1.9% (true positive)
Interpretation: Even with a positive test result, the actual probability of having the disease depends on prevalence.
Scenario: 30% chance of rain (P(A)), 60% chance of clouds (P(B)), with 25% chance of rain when cloudy (P(A|B))
Calculation: P(A∩B) = P(A|B) × P(B) = 0.25 × 0.6 = 15%
Interpretation: There's a 15% chance of both rain and clouds occurring together.
Scenario: System with two independent components each with 90% reliability (P(A)=P(B)=90%)
Calculation: P(A∪B) = 0.9 + 0.9 - (0.9×0.9) = 99% system reliability
Interpretation: The system has a 99% chance of working if at least one component must work.
Note: This calculator provides probability estimates based on standard probability theory. Real-world probabilities may vary based on additional factors not accounted for in these calculations.