Basic Probability Calculator
Enter event counts or probabilities to obtain complements, unions, intersections, and conditional probabilities. The tool highlights mutual exclusivity and independence, while providing Venn-style summaries and explanatory steps.
1. Choose Input Type & Enter Values
Probability Summary
Results readyKey Probabilities
- P(A)
- P(B)
- P(A ∩ B)
- P(A ∪ B)
- P(A')
- P(B')
Conditional & Diagnostic
- P(A | B)
- P(B | A)
- Mutually exclusive?
- Independent?
Venn Summary
| Only A | |
|---|---|
| Only B | |
| Both A & B | |
| Neither |
Step-by-Step Explanation
Formula Reference
Single event
\\[ P(A) = \\frac{\\text{favourable outcomes}}{\\text{total equally likely outcomes}} \\]
Complement
\\[ P(A') = 1 - P(A) \\]
Union of two events
\\[ P(A \\cup B) = P(A) + P(B) - P(A \\cap B) \\]
Conditional probability
\\[ P(A \\mid B) = \\frac{P(A \\cap B)}{P(B)}, \\qquad P(B) > 0 \\]
Events are independent when \\(P(A \\cap B) = P(A)P(B)\\).
Step-by-Step Guide
- Enter total outcome counts or direct probabilities and validate their bounds.
- Apply assumptions (mutual exclusivity, independence) when appropriate.
- Compute complements, unions, intersections, and conditional probabilities automatically.
- Inspect Venn-style breakdowns for “only A”, “only B”, “both”, and “neither”.
- Use the narrated steps to explain classroom reasoning or QA checks.
References
- Ross, S. M. (2014). A First Course in Probability (9th ed.). Pearson.
- Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Duxbury.