Probability Calculator
Calculate simple probability from favorable and total outcomes, as a percentage, decimal, and simplified fraction, with the complement and step-by-step working.
Outcomes that satisfy the event, e.g. rolling a 4.
All equally likely outcomes in the sample space, e.g. 6 for a die.
Probability
The event has a 25% probability of occurring, assuming each of the 12 outcomes is equally likely.
Decimal
0.25
Fraction
1/4
3/12 simplified
Complement P(not E)
75%
0.75 = 3/4
If the probability of the event is 25%, the probability that it does not occur is 75%, because P(not E) = 1 − P(E). A probability describes how likely the event is on a single trial under these assumptions; it does not guarantee how often it happens in any particular set of trials.
Favorable vs. unfavorable outcomes
- Favorable outcomes: 3
- Unfavorable outcomes: 12 − 3 = 9
Odds in favor: 3 : 9 = 1 : 3. Odds against: 3 : 1.
Odds compare favorable with unfavorable outcomes, while probability compares favorable with total outcomes. Odds of 1 : 3 are not a probability of 1/3; the probability here is 1/4.
How was this calculated?
Step 1 — Identify favorable outcomes
f = 3
Step 2 — Identify total outcomes
n = 12
Step 3 — Apply the probability formula
P(E) = favorable outcomes / total outcomes = f / n
This applies when every outcome is equally likely.
Step 4 — Substitute the values
P(E) = 3/12 = 1/4
Divide the numerator and denominator by their greatest common factor, 3, to simplify.
Step 5 — Convert to a decimal
P(E) = 3 ÷ 12 = 0.25
Step 6 — Convert to a percentage
0.25 × 100 = 25%
Result
P(E) = 1/4 = 0.25 = 25%
Where this result falls on the probability scale
| Probability | Meaning |
|---|---|
| 0 | Impossible under the model |
| 0 < P < 0.5 | Less likely than not ← this result |
| 0.5 | Even chance |
| 0.5 < P < 1 | More likely than not |
| 1 | Certain under the model |
Working with the fraction? Use the Fraction Calculator, or the Percentage Calculator for percentage conversions. When the outcomes themselves need counting, use the Combination Calculator for selections where order does not matter, or the Permutation Calculator for ordered arrangements.
This probability calculator finds the probability of an event from the number of favorable outcomes and the total number of possible outcomes. It shows the answer as a percentage, a decimal, and a simplified fraction, along with the complement (the probability the event does not occur), the favorable-to-unfavorable odds, and every step of the calculation.
It is built for simple probability with equally likely outcomes, such as coin flips, dice rolls, and card draws. Enter the two counts and the result appears instantly.
Worked Calculation Examples
| Scenario | Result | Calculation Step |
|---|---|---|
| Coin: probability of heads | 1/2 = 0.5 = 50% | A fair coin has 2 equally likely outcomes, and 1 is heads. P(H) = 1/2 = 0.5 = 50%. |
| Die: rolling a 4 | 1/6 ≈ 16.67% | A fair six-sided die has 6 outcomes, and 1 is a 4. P(4) = 1/6 ≈ 0.1667 ≈ 16.67%. Complement: 5/6 ≈ 83.33%. |
| Die: rolling an even number | 1/2 = 50% | The even outcomes are 2, 4, and 6, so 3 of the 6 outcomes are favorable. P = 3/6 = 1/2 = 50%. |
| Cards: drawing an ace | 1/13 ≈ 7.69% | A standard 52-card deck has 4 aces. P(A) = 4/52 = 1/13 ≈ 0.0769 ≈ 7.69%. |
| Simple ratio | 3/4 = 0.75 = 75% | 15/20 simplifies to 3/4 by dividing both by 5. P = 0.75 = 75%. |
| Impossible event | 0% | None of the 10 outcomes is favorable, so P = 0/10 = 0. The complement is 100%. |
| Certain event | 100% | All 10 outcomes are favorable, so P = 10/10 = 1 = 100%. The complement is 0%. |
What Is Probability?
Probability is a measure of how likely an event is to occur. It ranges from 0 to 1, or equivalently from 0% to 100%. A probability of 0 means the event is impossible under the model, 0.5 means an even chance, and 1 means the event is certain under the model.
Favorable outcomes are the outcomes that satisfy the event being considered. Total outcomes are all the possible outcomes in the sample space. When those outcomes are equally likely, the probability is their ratio: P(E) = f / n. For rolling a 4 on a fair six-sided die, f = 1 and n = 6, so P(4) = 1/6 ≈ 0.1667 ≈ 16.67%, and the complement, not rolling a 4, is 5/6 ≈ 83.33%.
Probability as a Fraction, Decimal, and Percentage
The same probability can be written three ways. 1/4 as a fraction is 0.25 as a decimal and 25% as a percentage. To convert, percentage = decimal × 100, and decimal = percentage ÷ 100. Probability is usually written as a decimal between 0 and 1 in mathematics, while percentages from 0% to 100% are often easier to read.
A 25% probability means the event has probability 0.25 on a trial under the stated assumptions. It does not mean the event happens exactly once in every four attempts: over many repeated, independent trials the proportion of successes tends toward 0.25, but any individual outcome remains uncertain.
Probability vs. Odds
Probability compares favorable outcomes with total outcomes: P(E) = favorable / total. Odds in favor compare favorable outcomes with unfavorable outcomes: favorable : unfavorable. With 25 favorable and 75 unfavorable outcomes out of 100, the probability is 25/100 = 25%, while the odds in favor are 25 : 75 = 1 : 3, and the odds against are 3 : 1.
Odds of 1 : 3 are not a probability of 1/3. To turn odds of a : b into a probability, divide a by a + b: 1 ÷ (1 + 3) = 1/4.
When Do You Need Permutations or Combinations?
Simple probability starts with favorable outcomes ÷ total outcomes, but sometimes those counts have to be worked out first. When the outcomes are selections where order does not matter, such as choosing 3 people from a group of 10, combinations count them. When order matters, such as arranging books on a shelf or the finishing order in a race, permutations count them. Use the Combination Calculator or Permutation Calculator to find the counts, then enter them here.
Problems involving conditional probability, several dependent events, or repeated trials (such as the binomial distribution) need different formulas than this simple ratio.
How to Use the Probability Calculator
- Enter the number of favorable outcomes: the outcomes that count as the event happening.
- Enter the total number of possible outcomes, all assumed equally likely.
- Make sure favorable outcomes are not greater than total outcomes. Both must be whole numbers.
- Review the probability as a percentage and a decimal. The result updates as you type.
- Review the simplified fraction, the complement (the chance the event does not occur), and the favorable-to-unfavorable odds.
- Read "How was this calculated?" to see each step from the formula to the percentage.
Frequently Asked Questions
What is probability?
Probability is a measure of how likely an event is to occur, on a scale from 0 (impossible) to 1 (certain), or 0% to 100%.
How do you calculate simple probability?
Divide the number of favorable outcomes by the total number of possible outcomes: P(E) = favorable outcomes / total outcomes. This works when every outcome is equally likely, such as the faces of a fair die.
What is the probability formula?
For equally likely outcomes, P(E) = f / n, where f is the number of favorable outcomes and n is the total number of possible outcomes. For example, the probability of drawing an ace from a standard 52-card deck is 4/52 = 1/13.
Can probability be 0?
Yes. A probability of 0 means the event is impossible under the model, because none of the possible outcomes is favorable. For example, rolling a 7 on a standard six-sided die has probability 0.
Can probability be 1?
Yes. A probability of 1 (100%) means the event is certain under the model, because every possible outcome is favorable. For example, rolling a number from 1 to 6 on a standard die has probability 1.
Can probability be greater than 100%?
No. A valid probability lies between 0 and 1, or 0% and 100%. The favorable outcomes can never outnumber the total outcomes, so the ratio can never exceed 1.
What is the difference between probability and odds?
Probability compares favorable outcomes with total outcomes, while odds in favor compare favorable outcomes with unfavorable outcomes. With 1 favorable and 3 unfavorable outcomes, the probability is 1/4 = 25%, but the odds in favor are 1 : 3.
How do you convert probability to a percentage?
Multiply the decimal probability by 100. For example, 0.25 × 100 = 25%.
How do you convert a probability percentage to a decimal?
Divide the percentage by 100. For example, 25% ÷ 100 = 0.25.
What does a 25% probability mean?
It means the event has probability 0.25 on a trial under the stated assumptions. It does not guarantee the event happens once in every four trials; over many repeated trials the proportion of successes tends toward 25%, but individual outcomes remain uncertain.
What is the probability of an impossible event?
The probability of an impossible event is 0, or 0%.
What is the probability of a certain event?
The probability of a certain event is 1, or 100%.
Does this calculator handle conditional probability?
No. This calculator is designed for simple probability from favorable and total outcomes. Conditional probability, the probability of one event given that another has occurred, needs a different formula: P(A | B) = P(A and B) ÷ P(B).
When should I use permutations or combinations?
Use them when you first need to count the outcomes. Combinations count selections where order does not matter, and permutations count arrangements where order does matter. Find the counts with the Combination Calculator or Permutation Calculator, then enter them here.
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Last updated: September 27, 2026.