π Statistics & Probability
Probability Calculator
Compute binomial probability, single-event probability, and combinations. Free probability calculator for AP Stats and analysts.
What This Calculator Tells You
Probability is the chance an event happens, from 0 (impossible) to 1 (certain). This calculator handles the most common everyday case: equally likely outcomes. Enter how many outcomes count as a success and how many are possible, and it gives the probability and the odds.
Add a number of independent trials and it also tells you the chance of the event happening at least once β the question behind 'what are the chances I roll a six in four tries?' or 'how likely is at least one defect in 50 units?'
What to Enter
- Favorable outcomes β the outcomes that count as success (e.g. 1 face on a die, 4 aces in a deck).
- Total outcomes β all equally likely possible outcomes (6 faces, 52 cards).
- Independent trials (optional) β how many times the event is attempted, where each attempt does not affect the others.
Worked Examples
1. Rolling a six
1 favorable out of 6, over 4 rolls.
- Single roll: 16.67%, odds 1:5.
- At least one six in 4 rolls: 51.77% β slightly better than a coin flip.
2. Quality control
A 2% defect rate (2 in 100), checking 50 independent units.
- Chance of at least one defect: 63.58%.
3. Drawing an ace
4 favorable out of 52.
- 7.69%, odds 4:48 (1:12).
How It’s Calculated
- P: Principal amount
- k: Compounding periods per year / count
- n: Number of periods or sample size
- C: Variable C
- p: Sample proportion / p-value
How to Read Your Result
- Probability vs odds: a 25% probability is odds of 1:3 (one success for every three failures).
- 'At least once' = 1 β (1 β p)n. Small risks add up fast over many trials.
- Independence matters. Drawing cards without putting them back changes the odds each time; this tool assumes independent trials.
- Probabilities under 1% are shown with extra decimals so rare events are not rounded to zero.
Common Mistakes to Avoid
- Adding probabilities across trials. Four rolls do not give 4 Γ 16.7% = 66.7%; the correct answer is 51.8%.
- The gambler's fallacy. After five tails, the next coin flip is still 50%.
- Using unequal outcomes. This method needs every outcome to be equally likely.
- Confusing odds with probability when reading betting lines.
When to Use This Calculator
- Solve homework and exam probability questions.
- Estimate the chance of at least one failure, defect or incident.
- Understand game, lottery or raffle odds.
- Explain risk in plain numbers to a team.
Frequently Asked Questions
How do you calculate probability?
Probability = favorable outcomes Γ· total possible outcomes, when all outcomes are equally likely.
How do you calculate the probability of at least one success?
P(at least one) = 1 β (1 β p)n, where p is the single-trial probability and n the number of independent trials.
What is the difference between probability and odds?
Probability is successes Γ· all outcomes. Odds compare successes with failures. 1 in 4 probability = 1:3 odds.
Can this handle dependent events?
Not directly. For draws without replacement, multiply the changing probabilities step by step or use combinations.
Do you store the values I enter?
No. All calculations happen in your browser. Your data never leaves your device.
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