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Statistics Tool

Probability Calculator

Calculate single-event, multi-event, independent, and dependent probabilities. Evaluate union (A or B), intersection (A and B), and conditional likelihoods.

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Interactive Probability Calculator Workspace

Live Solver
Probability P(A)25.00% (0.2500)

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

Equation ModelP(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

SymbolDescription
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).

Step 1: For independent events, Intersection P(A ∩ B) = P(A) * P(B) = 0.50 * 0.20 = 0.10.
Step 2: Calculate Union P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.50 + 0.20 - 0.10 = 0.60.
Step 3: Calculate P(A) Complement P(A') = 1 - 0.50 = 0.50.
The probability of either event happening P(A ∪ B) is 60% (0.6000).

Frequently Asked Questions

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