Probability Calculator
Free online Probability Calculator to find the odds of single and combined events instantly.
Result
| No of possible event that occured | ||
|---|---|---|
| No of possible event that do not occured |
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The Probability Calculator works out the likelihood of single and combined events instantly — including the chance of two events both happening, either one happening, and an event not happening. Enter your probabilities, pick the relationship, and get an accurate result without wrestling with the formulas yourself.
Probability, Made Practical
Probability turns uncertainty into a number between 0 and 1 (or 0% and 100%). The single-event case is easy, but the real power — and the real confusion — comes from combining events. This calculator handles the combinations cleanly so you can answer "what are the odds of both?" or "either?" with confidence.
How to Use It
- Enter each event's probability as a decimal or percent.
- Choose the relationship — single, both (AND), or either (OR).
- Read the calculated probability.
The Core Rules of Probability
| Question | Rule | Example |
|---|---|---|
| Both A and B | P(A) × P(B) | 0.5 × 0.4 = 0.20 |
| Either A or B | P(A) + P(B) − P(A and B) | 0.5 + 0.4 − 0.2 = 0.70 |
| Not A | 1 − P(A) | 1 − 0.3 = 0.70 |
Why "Both" Makes Things Less Likely
Multiplying two probabilities always yields a smaller number, and that's exactly right: requiring two things to happen together is harder than requiring just one. The chance of flipping two heads in a row (0.5 × 0.5 = 0.25) is lower than a single heads. The multiplication rule captures this, but it assumes the events are independent — one doesn't change the other.
Why "Either" Subtracts the Overlap
For "A or B," simply adding the probabilities would double-count the cases where both occur. Subtracting P(A and B) corrects this, keeping the total honest and never letting it exceed what's truly possible. This is the addition rule, and it's the source of many textbook mistakes when the overlap is ignored.
The Underrated Power of the Complement
Many "at least one" problems are far easier solved backward. Instead of adding up every way something can happen, calculate the chance it doesn't happen and subtract from 1. For "at least one success in several tries," the complement — the chance of all failures — is usually a single quick multiplication.
Independent vs. Dependent Events
The multiplication rule here assumes independence, like coin flips or dice. When events are dependent — drawing cards without replacing them, for example — each outcome changes the remaining odds, and the math must adjust accordingly. Knowing which situation you're in is the key to a correct answer.
Free and Private
All calculations run locally in your browser. Use it for games of chance, risk estimates, quality control, or any decision where likelihoods combine — free and unlimited.
Frequently Asked Questions
What is probability?
Probability is a measure of how likely an event is, expressed from 0 (impossible) to 1 (certain), or equivalently from 0% to 100%. A probability of 0.5 means an event is as likely to happen as not.
How do I calculate the probability of two events both happening?
For independent events, multiply their individual probabilities. If event A is 0.5 and event B is 0.4, the chance of both is 0.5 × 0.4 = 0.2, or 20%. Multiplying makes the combined chance smaller, which matches intuition.
How do I calculate the probability of either event happening?
For the chance of A or B, add their probabilities and subtract the probability of both, so you don't double-count the overlap: P(A) + P(B) − P(A and B). This 'or' rule prevents the total from exceeding the true likelihood.
What is the complement of an event?
The complement is the probability that an event does not happen, calculated as 1 minus the event's probability. If rain is 0.3 likely, no rain is 0.7. Complements are often the easiest path to 'at least one' problems.
What is the difference between independent and dependent events?
Independent events don't affect each other — coin flips, for instance. Dependent events do, like drawing cards without replacement, where each draw changes the remaining odds. The multiplication rule shown here assumes independence.
Can I enter probabilities as percentages?
Yes. You can work in decimals (0.25) or percentages (25%); just stay consistent. The calculator treats them equivalently and returns a clear result either way.
Is this useful for real decisions?
Yes — for risk assessment, games of chance, quality control, and any situation where you combine likelihoods. It turns vague hunches about 'how likely' into concrete numbers you can reason with.
Is this tool free?
Yes, completely free with no signup and no limits.