Probability Calculator
Calculate probabilities including complements, unions, intersections, and conditional probabilities. Learn probability rules with step-by-step solutions.
Probability Rules Reference
Complement Rule:
P(A') = 1 - P(A)
Addition Rule:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Multiplication Rule (Independent):
P(A ∩ B) = P(A) × P(B)
Conditional Probability:
P(A|B) = P(A ∩ B) / P(B)
Probability Calculations
This calculator helps you compute various types of probabilities using fundamental probability rules.
Types of Calculations
Basic Probability
Simply displays the probability value you enter, useful for reference.
Complement
Calculates P(A’) = 1 - P(A), the probability that event A does NOT occur.
Union (A ∪ B)
Calculates the probability that A OR B (or both) occurs using the addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Intersection (A ∩ B)
For independent events, calculates the probability that BOTH A and B occur: P(A ∩ B) = P(A) × P(B)
Conditional (A|B)
Calculates the probability of A given that B has occurred: P(A|B) = P(A ∩ B) / P(B)
Probability Rules Summary
| Rule | Formula | Description |
|---|---|---|
| Complement | P(A’) = 1 - P(A) | Probability A doesn’t occur |
| Addition | P(A∪B) = P(A) + P(B) - P(A∩B) | Either A or B occurs |
| Multiplication (independent) | P(A∩B) = P(A) × P(B) | Both A and B occur |
| Conditional | P(A|B) = P(A∩B) / P(B) | A occurs given B occurred |
Important Notes
- All probabilities must be between 0 and 1
- The intersection formula assumes independence
- For dependent events, use the conditional probability formula
- P(A|B) is usually different from P(B|A)
Applications
- Risk assessment
- Quality control
- Medical diagnosis
- Financial modeling
- Game theory
- Machine learning
Related Tools
- Z-Score Calculator - Calculate standard scores
- T-Test Calculator - Hypothesis testing
Want to learn the theory?
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