Understanding Probability as a Fraction
Probability expressed as a fraction shows the ratio of favorable outcomes to total possible outcomes. For example, when rolling a standard die, the probability of getting a 6 is 1/6, meaning there is 1 favorable outcome out of 6 possible outcomes.
Fractions are often the most intuitive way to express probability because they directly show the relationship between favorable and total outcomes. This calculator converts between fractions, decimals, percentages, and odds formats, and simplifies fractions to their lowest terms using the greatest common divisor (GCD).
Conversion Formulas
Common Probabilities
| Event | Fraction | Decimal | Percentage |
|---|---|---|---|
| Coin flip (heads) | 1/2 | 0.500 | 50% |
| Die roll (any number) | 1/6 | 0.167 | 16.67% |
| Card draw (ace) | 4/52 = 1/13 | 0.077 | 7.69% |
| Card draw (heart) | 13/52 = 1/4 | 0.250 | 25% |
Frequently Asked Questions
How do I simplify a probability fraction?
Divide both the numerator (favorable outcomes) and denominator (total outcomes) by their greatest common divisor (GCD). For example, 4/52: the GCD of 4 and 52 is 4, so 4/52 simplifies to 1/13.
What is the difference between probability and odds?
Probability is the ratio of favorable outcomes to total outcomes (e.g., 1/4 = 25%). Odds compare favorable outcomes to unfavorable outcomes (e.g., 1:3 means 1 favorable for every 3 unfavorable). While probability ranges from 0 to 1, odds range from 0 to infinity.