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Probability Calculator

Calculate probability of single events, multiple events, conditional probability, and odds.

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Single Event Probability

Example: Rolling a 1, 2, or 3 on a six-sided die → 3 favorable, 6 total

Probability Rules

  • Range: 0 ≤ P(A) ≤ 1 (or 0% to 100%)
  • Complement: P(A') = 1 - P(A)
  • AND (independent): P(A ∩ B) = P(A) × P(B)
  • OR: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
  • Conditional: P(A|B) = P(A ∩ B) / P(B)
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How to Use This Calculator

  1. Choose the calculation mode: Single Event (basic probability), Multiple Events (AND/OR), or Conditional Probability
  2. For single events: enter the number of favorable outcomes and total possible outcomes
  3. For multiple events: enter individual probabilities and select whether events are independent and whether you want AND or OR
  4. For conditional probability: enter P(A), P(B), and P(A∩B) to find P(A|B) and P(B|A)
  5. Click Calculate to see the probability as a decimal, percentage, and additional insights

Formula

Single Event: P = favorable/total | AND (independent): P(A∩B) = P(A)×P(B) | OR: P(A∪B) = P(A)+P(B)-P(A∩B) | Conditional: P(A|B) = P(A∩B)/P(B) | Complement: P(A') = 1-P(A)

Frequently Asked Questions

What is probability?▼
Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). It can also be expressed as a percentage (0% to 100%).
What's the difference between 'AND' and 'OR' probability?▼
'AND' probability (intersection) is the chance that both events occur together. 'OR' probability (union) is the chance that at least one event occurs. AND uses multiplication, OR uses addition minus the overlap.
What does independent vs dependent events mean?▼
Independent events don't affect each other (like coin flips). Dependent events influence each other (like drawing cards without replacement). For independent events, P(A and B) = P(A) × P(B).
What is conditional probability?▼
Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It's calculated as P(A∩B)/P(B), showing how one event affects another.
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