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Probability Calculator

Calculate single event probabilities, odds ratios, complementary chances, and independent multi-event unions and intersections.

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How to Use the Probability Calculator – Event Odds & Likelihood

1Enter the number of favorable favorable outcomes (Event A).
2Enter the total number of possible exhaustive outcomes.
3Read the probability P(A), percentage chance, complementary probability P(not A), and odds ratio.
4Review the step-by-step probability formulas and interpretations.

Formula & How It Works

Classical Theoretical Probability Model

P(A) = Favorable Outcomes ÷ Total Outcomes | P(not A) = 1 - P(A)

For equally likely outcomes, the probability of event A is the number of favorable outcomes n(A) divided by total outcomes n(S). Complementary probability P(A') = 1 - P(A). Odds in favor are expressed as n(A) to (n(S) - n(A)).

Worked Examples

Standard Six-Sided Die Roll

Input: Favorable: 1 (rolling a 4), Total: 6

Explanation: 1 favorable outcome out of 6 possible sides yields 1/6 ≈ 16.67%.

Result: P(A) = 0.1667 (16.67%) | Odds: 1 to 5 | P(not A) = 83.33%

Drawing an Ace from a Card Deck

Input: Favorable: 4 aces, Total: 52 cards

Explanation: 4 / 52 reduces to 1/13 ≈ 7.69% probability.

Result: P(A) = 0.0769 (7.69%) | Odds: 1 to 12 | P(not A) = 92.31%

Coin Toss Heads

Input: Favorable: 1 head, Total: 2 sides

Explanation: 1 / 2 = 0.50 or an even 50-50 chance.

Result: P(A) = 0.5000 (50.00%) | Odds: 1 to 1 (Even)

Certain Event Benchmark

Input: Favorable: 10, Total: 10

Explanation: When favorable outcomes equal total outcomes, the event is guaranteed to happen.

Result: P(A) = 1.0000 (100.00%) | Complement: 0.00%

Frequently Asked Questions

What is the difference between probability and odds?▼

Probability is the ratio of favorable outcomes to all outcomes (P = A / Total). Odds compare favorable outcomes directly against unfavorable outcomes (Odds = A : Not A).

Can a probability be greater than 1 or negative?▼

No, by mathematical definition, probability must always lie between 0 (impossible event) and 1 (certain event), or 0% to 100%.

What is complementary probability?▼

The complement of an event A is the probability that event A does NOT occur: P(not A) = 1 - P(A).

How do you calculate independent events happening together?▼

For independent events A and B, multiply their probabilities: P(A and B) = P(A) × P(B).

Can favorable outcomes exceed total outcomes?▼

No, favorable outcomes cannot be greater than the total number of possible outcomes.

Does this tool work completely offline?▼

Yes, all probability calculations run locally in your web browser with zero server latency.

Last reviewed & updated: 2026-11-01

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