Probability Fraction Calculator
Convert probability to fraction form with automatic simplification
Calculate Probability Fractions
Event Outcomes
Please enter at least one outcome with a count greater than 0 to calculate probabilities.
Example: Coin Toss Results
Problem
Scenario: You toss a coin 1000 times
Results: Heads = 504 times, Tails = 496 times
Total events: 1000
Solution
P(Heads): 504/1000 = 63/125 (simplified) = 0.504 = 50.4%
P(Tails): 496/1000 = 62/125 (simplified) = 0.496 = 49.6%
Verification: 63/125 + 62/125 = 125/125 = 1 ✓
Probability Formulas
Basic Probability
P(A) = n_A / n_totalWhere n_A is the number of favorable outcomes and n_total is the total number of outcomes.
Fraction Simplification
a/b = (a÷gcd)/(b÷gcd)Divide both numerator and denominator by their greatest common divisor.
Probability Representations
Fraction
Exact ratio representation (3/4)
Decimal
Decimal representation (0.75)
Percentage
Percentage representation (75%)
Quick Tips
Probabilities always sum to 1 for all possible outcomes
Simplify fractions by finding the GCD of numerator and denominator
Probability values range from 0 (impossible) to 1 (certain)
Fractions provide exact representations without rounding errors
Understanding Probability Fractions
What is Probability as a Fraction?
Probability as a fraction expresses the likelihood of an event as a ratio between favorable outcomes and total possible outcomes. This representation provides exact values without decimal rounding errors.
Why Use Fractions?
- •Exact representation without rounding errors
- •Easy comparison with unit fractions
- •Clear visualization of likelihood magnitude
- •Simplified form reveals common patterns
Calculation Steps
- Count favorable outcomes for each event
- Count total number of trials or observations
- Write probability as fraction: n_favorable / n_total
- Find GCD of numerator and denominator
- Simplify by dividing both by GCD
Multiple Events
For multiple outcomes A, B, C: P(A) + P(B) + P(C) = 1 when they represent all possible outcomes. Each probability is calculated as n_outcome / n_total.