Probability Calculator
Calculate single-event, multi-event, independent, and dependent probabilities. Evaluate union (A or B), intersection (A and B), and conditional likelihoods.
Interactive Probability Calculator Workspace
Step-by-Step Probabilities
Step 1: Calculate standard probability formula:
P(A) = favorable / total = 5 / 20 = 0.2500
Step 2: Calculate the complement (likelihood of event A NOT occurring):
P(A') = 1 - P(A) = 1 - 0.2500 = 0.7500 (or 75.00%)
Mathematical Formula & Variables
P(A) = n(A) / n(S) | P(A ∪ B) = P(A) + P(B) - P(A ∩ B)The probability of an event is the ratio of favorable outcomes to total possible outcomes in a sample space. The union formula calculates the likelihood of either event happening.
Variable Definitions
| Symbol | Description |
|---|---|
| P(A) | Probability of event A |
| P(B) | Probability of event B |
| P(A ∩ B) | Probability of both A and B occurring (Intersection) |
| P(A ∪ B) | Probability of either A or B occurring (Union) |
| P(A|B) | Conditional probability of A given that B occurred |
How to Use the Probability Calculator
- Select your calculation mode (Single Event, Two Independent Events, or Two General Events).
- Input the individual probabilities or raw frequencies as requested.
- The tool computes the Union, Intersection, Complement, and conditional probabilities automatically.
Practical Example Calculation
Scenario Context: Calculating independent event probabilities where P(A) = 0.50 (tossing heads) and P(B) = 0.20 (rolling a 6 on a custom die).
Frequently Asked Questions
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