Probability Calculator
Single events, and/or, at-least-once & nCr/nPr — with dice/coin/card presets, odds, fractions & textbook steps.
Classic scenarios
💡 Try the presets — dice, coins, and cards cover most homework questions.
P(event) = 1/6
16.6667%
Decimal
0.1667
Complement
83.3333%
Odds for
1 : 5
Step-by-step working
1. P(event) = favourable ÷ total = 1 ÷ 6
2. = 1/6 = 0.1667 = 16.6667%
3. Complement: P(not event) = 1 − 0.1667 = 0.8333 (83.3333%)
📊 How likely is that?
Your event on the 0–100% likelihood line.
⚠️ The two-event formulas assume independence; for dependent events (drawing cards without replacement) multiply the changing per-step probabilities instead.
🎲Four probability questions, every step shown
Everything a probability chapter asks, with the working written out: single events (with one-click dice, coin, and card presets, plus simplified fractions, complements, and odds), two independent events combined with AND/OR, the classic "at least once in n tries" question solved by the complement trick, and nCr / nPr combinatorics with the cancellation shown. Each answer comes as a fraction, decimal, and percentage, placed on a visual likelihood line.
📊Everything you'd want to know
- Single events: simplified fraction, decimal, percentage, complement, and odds-for — all at once.
- Presets for the classics: coins, dice (six or even), aces, hearts, and face cards.
- AND/OR for independent events, with the double-count subtraction explained.
- 'At least once' via 1 − P(never) — the trick that unlocks half of all word problems.
- nCr and nPr side by side, with when-order-matters guidance.
- Copy-the-working button for homework, and a likelihood line for intuition.
🧮The formulas
The OR formula subtracts the overlap so outcomes where both happen aren't counted twice. The at-least-once trick works because "at least one" and "none" split all possibilities between them — computing the easy one gives the hard one for free.
💡Traps worth knowing
- Independence matters: drawing two cards without replacement changes the second probability — multiply step-by-step instead.
- 'And' multiplies, 'or' adds (minus overlap) — swapping them is the most common exam error.
- Odds and probability differ: 1:5 odds-for means P = 1/6, not 1/5.
- Past outcomes don't change fair dice — the gambler's fallacy costs real money.
💡 Frequently Asked Questions
How do I calculate probability?+
Divide favourable outcomes by total possible outcomes: P = favourable ÷ total. Rolling a six is 1/6 ≈ 16.67%. This calculator shows the simplified fraction, decimal, percentage, complement, and odds together, with steps.
What is the probability of getting at least one six in 4 rolls?+
1 − (5/6)⁴ ≈ 51.77%. Compute the probability of missing every time, then subtract from 1 — the 'at least once' mode applies this complement trick to any probability and any number of tries.
What is the difference between nCr and nPr?+
Both count ways to pick r items from n. nPr counts ordered arrangements (trophies: 1st, 2nd, 3rd); nCr counts unordered groups (a team of 3). nCr = nPr ÷ r!, and the calculator shows both with that division made explicit.
How do I combine the probability of two events?+
For independent events: P(A and B) = P(A) × P(B), and P(A or B) = P(A) + P(B) − P(A and B). The subtraction removes the double-counted overlap. For dependent events, multiply the updated probabilities step by step.
How do I convert probability to odds?+
Odds-for = favourable : unfavourable. A 1/6 probability is 1:5 odds — one way to win against five ways to lose. The single-event mode reports both formats simultaneously.