Probabilities are often clearest as fractions. If a bag holds 6 red, 4 blue, 8 green and 2 yellow marbles, the chance of red is 6/20, which simplifies to 3/10. Fractions keep the exact value – no rounding – and make it easy to see how outcomes compare: red is 3/10, green 2/5 and yellow 1/10.
Type the counts of each outcome (how many marbles, survey answers, observed results) and, optionally, their names. The calculator adds the counts to get the total, writes each probability as count/total, reduces it by the greatest common divisor, and gives the decimal and percentage alongside. The fractions of all outcomes always add up to 1, which the pie chart shows visually.
The same method works for theoretical counts (the 6 faces of a die) and for experimental ones (the results of 50 spins), but remember that observed frequencies are estimates and will vary from one experiment to the next.
How to use the Probability Fraction Calculator
- Outcome names (optional, comma-separated)
- Count of each outcome (same order)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Each count is divided by the sum of all counts. The fraction is reduced with Euclid’s algorithm for the greatest common divisor, and the decimal and percentage are computed from the same ratio.
Worked example
A bag holds 6 red, 4 blue, 8 green and 2 yellow marbles, 20 in total. P(red) = 6/20 = 3/10 = 0.3 = 30%; P(blue) = 4/20 = 1/5 = 20%; P(green) = 8/20 = 2/5 = 40%; P(yellow) = 2/20 = 1/10 = 10%. Green is the most likely colour, and the four fractions add up to 1.
Common probability fractions
| Event | Fraction | Percent |
|---|---|---|
| Heads on a coin | 1/2 | 50% |
| A six on a die | 1/6 | 16.67% |
| A heart from a deck | 13/52 = 1/4 | 25% |
| An ace from a deck | 4/52 = 1/13 | 7.69% |
Formula
P(outcome) = count of the outcome ÷ total count
Simplify: divide numerator and denominator by their greatest common divisor
Worked example
Inputs — Outcome names (optional, comma-separated): Red, Blue, Green, Yellow; Count of each outcome (same order): 6, 4, 8, 2.
Results — Probability of the first outcome = Red: 6/20 = 3/10; As a decimal = 0.3; As a percentage = 30 %; Total count (denominator) = 20; Most likely outcome = Green (2/5, 40%); All outcomes = Outcome Count Fraction Simplified Decimal Percent
───────────────────────────────────────────────────────────
Red 6 6/20 3/10 0.3 30%
Blue 4 4/20 1/5 0.2 20%
Green 8 8/20 2/5 0.4 40%
Yellow 2 2/20 1/10 0.1 10%.
Key terms
- Probability fraction
- A probability written as favourable ÷ total outcomes.
- Greatest common divisor
- The largest whole number that divides both numerator and denominator.
- Relative frequency
- An observed count divided by the total number of trials.
Frequently asked questions
How do I write a probability as a fraction?
Put the number of favourable outcomes over the total number of outcomes, then simplify. 6 red out of 20 marbles is 6/20 = 3/10.
How do I simplify a probability fraction?
Divide top and bottom by their greatest common divisor. For 6/20 the GCD is 2, giving 3/10.
What is the probability of rolling an even number as a fraction?
3/6 = 1/2.
Do the fractions have to add up to 1?
Yes, for a complete set of outcomes. Here 3/10 + 1/5 + 2/5 + 1/10 = 1.
How do I convert a probability fraction to a percentage?
Divide and multiply by 100: 3/10 = 0.3 = 30%.
How many outcomes can I enter?
Up to 20.