🎓 Statistics & Data • Probability & Distributions
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Probability Calculator (AND / OR Rules)
Solves compound probability problems using standard product and sum rules for independent and mutually exclusive events.
Event Probability Rules
Compound Probability & Venn Diagram
Compute Joint P(A ∩ B), Union P(A ∪ B), Conditional probabilities, and visual proportions for independent events.
P(A AND B) Joint0.2424%
P(A OR B) Union0.7676%
P(Not A)0.440%
P(Not B)0.660%
Visual Venn Diagram Proportions
Probability Rules
Probability quantifies likelihood from 0 (impossible) to 1 (certain). Compound probabilities combine multiple events through addition and multiplication.
Formula & Step-by-Step Calculation
P(A ∪ B) = P(A) + P(B) - P(A ∩ B), P(A ∩ B) = P(A) · P(B) [Independent]
General addition rule and multiplication rule.
Worked Step-by-Step Examples
Example 1
P(A) = 0.6, P(B) = 0.4 for independent events. Find P(A or B).
Solution: P(A or B) = 0.76 (76%)
• P(A and B) = 0.6 × 0.4 = 0.24; P(A or B) = 0.6 + 0.4 - 0.24 = 0.76
Common Real-World & Academic Use Cases
- ✓ Insurance underwriting risk assessment
- ✓ Gambling and lottery probability calculations
- ✓ Reliability engineering component failure rates
How to Use the Probability Calculator (AND / OR Rules)
1
Enter Event Probabilities
Input P(A) and P(B).
2
Read Outcomes
Inspect joint, union, and complement probabilities.
Frequently Asked Questions
Q: What is the difference between mutually exclusive and independent events?
Mutually exclusive events cannot happen at the same time; independent events do not affect each other's probability.