# Probability Calculator

Free probability calculator. Calculate the probability of an event from favorable and total outcomes. Find complement probability, percentages, and odds.

## What this calculates

Calculate the probability of an event occurring based on the number of favorable outcomes and total possible outcomes. Also shows the complement probability, percentage, and odds in favor and against.

## Inputs

- **Favorable Outcomes** — min 0 — The number of outcomes that satisfy the event.
- **Total Outcomes** — min 1 — The total number of equally likely outcomes.

## Outputs

- **Probability P(A)** — The probability of the event occurring.
- **Percentage** — formatted as percentage — The probability expressed as a percentage.
- **Complement P(A')** — The probability of the event NOT occurring.
- **Complement Percentage** — formatted as percentage — The complement probability as a percentage.
- **Odds** — formatted as text — The odds in favor and against the event.
- **Formula** — formatted as text — Step-by-step calculation.

## Details

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain).

Basic Probability Formula

P(A) = favorable outcomes / total outcomes

Complement Rule

P(A') = 1 - P(A)

The complement is the probability of the event NOT occurring. The probability of an event and its complement always sum to 1.

Odds vs Probability

- Probability: favorable / total (e.g., 1/6)

- Odds in favor: favorable : unfavorable (e.g., 1:5)

- Odds against: unfavorable : favorable (e.g., 5:1)

Examples

- Rolling a 6 on a fair die: P = 1/6 ≈ 16.67%

- Drawing an ace from a deck: P = 4/52 = 1/13 ≈ 7.69%

- Flipping heads on a fair coin: P = 1/2 = 50%

## Frequently Asked Questions

**Q: What is the difference between probability and odds?**

A: Probability is the ratio of favorable outcomes to total outcomes (e.g., 1/6 for rolling a specific number on a die). Odds compare favorable to unfavorable outcomes (e.g., 1:5 for rolling that number, meaning 1 way to succeed vs 5 ways to fail). To convert odds a:b to probability: P = a/(a+b).

**Q: What is complement probability?**

A: The complement of an event A is the event 'not A' (written A' or A-bar). P(A') = 1 - P(A). For example, if the probability of rain is 0.3, the probability of no rain is 1 - 0.3 = 0.7. The complement rule is useful when it is easier to calculate the probability of something NOT happening.

**Q: Can probability be greater than 1?**

A: No. Probability ranges from 0 to 1 (or 0% to 100%). A probability of 0 means the event is impossible, and 1 means it is certain. If your calculation gives a value outside this range, check your inputs -- favorable outcomes cannot exceed total outcomes.

**Q: What does 'equally likely outcomes' mean?**

A: This formula assumes all outcomes have the same chance of occurring (like a fair die or coin). If outcomes are not equally likely (e.g., a loaded die), you cannot simply divide favorable by total. You would need to know the individual probabilities of each outcome.

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Source: https://vastcalc.com/calculators/statistics/probability
Category: Statistics
Last updated: 2026-04-21