Probability Fraction Calculator

What Probability as a Fraction Means

Probability as a fraction compares successful outcomes to total outcomes. If 18 results out of 40 match event $A$, then the probability of $A$ is $18/40$, which simplifies to $9/20$. This calculator turns raw counts into simplified fractions, decimals, and percentages for several outcomes at once.

Probability Fraction Formula

$$P(A) = \frac{n_A}{n_{\text{total}}}$$

The numerator is the number of times outcome $A$ occurs. The denominator is the total number of observed outcomes across all categories.

Why Simplifying Fractions Helps

Simplified fractions make probability easier to compare and communicate. For example, $24/60$ and $2/5$ represent the same probability, but $2/5$ is easier to read. This tool automatically reduces each fraction by its greatest common divisor.

How To Use This Calculator

Choose how many outcomes you want to track.
Enter the count for each outcome.
Select which outcome you want to highlight.
Read the simplified fraction, decimal probability, and percentage for each row.

Related Probability Tools

If you need event unions or multi-event results, try the Probability Calculator, OR Probability Calculator, and Probability of 3 Events Calculator.

Frequently Asked Questions

Can probability be written as a fraction?

Yes. Probability is naturally a ratio, so fraction form is one of its most direct representations.

How do I simplify a probability fraction?

Divide both numerator and denominator by their greatest common divisor. This calculator does that automatically.

What if an outcome count is zero?

Its probability is zero. The calculator displays this cleanly while still using the same total denominator for every other outcome.

Do all displayed probabilities add up to 1?

Yes, as long as your listed outcomes cover the full set of observed results. Their decimals and percentages should sum to 1 or 100%.

When is fraction form better than percentage form?

Fraction form is useful in classroom work, combinatorics, and exact symbolic reasoning. Percentage form is often easier for quick interpretation.

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