Convert probability fractions to decimals, percentages, and odds. Simplify fractions, combine probabilities, compute binomial distribution over trials, and view equivalent fractions.
The probability fraction calculator converts between fractions, decimals, percentages, and odds — the four common ways to express probability. Enter a fraction like 3/8 and instantly see it as 0.375, 37.5%, or 3:5 odds in favor.
Beyond conversion, this calculator computes binomial probabilities over multiple trials: what's the chance of getting exactly 2 successes in 5 tries with probability 3/8? It also generates the full binomial distribution table with visual bars, shows equivalent fractions, and can combine two probability fractions using AND/OR operations.
Use presets for common fractions like dice rolls (1/6), card suits (13/52), or enter any numerator and denominator to explore. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results. Validate that outputs match your chosen standards. Run at least one manual sanity check before publishing.
Probability fractions appear everywhere — from classroom exercises to gambling odds, quality control to weather forecasts. This calculator bridges the gap between how people think about probability (fractions, percentages, odds) and the mathematical operations needed (simplification, combination, repeated trials).
The built-in binomial distribution shows what happens when you repeat a probabilistic event, making it a comprehensive tool for anyone working with discrete probabilities.
P = Numerator / Denominator. Simplified by dividing both by GCD. Odds = P / (1 − P). Binomial: P(X=k) = C(n,k) × p^k × (1−p)^(n−k).
Result: 37.5%, odds 3:5, P(exactly 2 in 5) = 31.15%
3/8 is already simplified (GCD = 1). As a decimal it's 0.375 or 37.5%. The odds in favor are 3:5. In 5 trials, the probability of exactly 2 successes is 31.15% using the binomial formula.
Probability fractions are the most intuitive representation. Drawing a heart from a deck: 13/52 = 1/4. Rolling a 6 on a die: 1/6. These fractions directly encode the counting principle: favorable outcomes divided by total outcomes. Converting to decimals or percentages is useful for comparison, but fractions preserve the underlying structure.
While individual trial outcomes are unpredictable, the average result converges to the expected value as trials increase. With P = 3/8, you might get 0 or 5 successes in 5 trials, but over 1,000 trials, the percentage will be very close to 37.5%. The binomial distribution quantifies exactly how much variation to expect at each sample size.
For independent events A and B: P(A AND B) = P(A) × P(B) and P(A OR B) = P(A) + P(B) − P(A)×P(B). With fractions, multiplication is straightforward (multiply numerators and denominators), while addition requires common denominators. This calculator handles both operations automatically.
Divide the numerator by the denominator. For 3/8: 3 ÷ 8 = 0.375 = 37.5%. The numerator represents favorable outcomes and the denominator total possible outcomes.
Probability is favorable/total (3/8 = 0.375). Odds are favorable/unfavorable (3:5 or 0.6:1). To convert odds to probability: odds/(1+odds). Odds of 3:5 = 3/(3+5) = 3/8.
Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. For 6/8: GCD(6,8)=2, so 6/8 simplifies to 3/4.
No, probability is always between 0 and 1 (0% to 100%). If your fraction exceeds 1, it represents something other than probability — check that favorable outcomes don't exceed total outcomes.
It calculates the probability of exactly k successes in n independent trials, each with probability p. For example, getting exactly 3 heads in 10 coin flips, or rolling exactly 2 sixes in 5 dice rolls.
Fractions that represent the same value: 1/2 = 2/4 = 3/6 = 50/100. Multiply both numerator and denominator by the same number to generate equivalents.