Probability Calculator
Work out probabilities for a single event, two independent events, or a repeated series of trials.
Details
Between 0% and 100%.
Chance it does NOT happen
75%
Because there is a 25% chance that it does
This works out the chance of events happening, whether that is a single event, two events together, or at least one success across a run of trials.
It returns the result as a percentage, a decimal and a 1-in-N figure, which is usually the form that actually means something.
How probability works
A probability is how likely something is, on a scale from 0 to 1. Zero means impossible, one means certain, and 0.5 means it happens half the time.
It is worked out as the number of ways the thing can happen divided by the total number of possible outcomes. One six on a die out of six faces gives 1/6, or about 16.7%.
The part that trips people up is combining events. AND multiplies, OR adds. Both things happening is rarer than either alone; either one happening is more likely than both.
Multiplying makes the answer smaller, which is correct: needing two things to go your way is harder than needing one. Adding them would give 1.0, which would mean certainty.
What to enter
- Scenario
- A single event, two independent events, or a series of trials where you want the chance of at least one success.
- Probability of A and B
- Enter each as a decimal (0.5) or a percentage (50%). Two events are independent if one has no effect on the other.
- Number of trials (n)
- How many attempts, for the series scenario. This is what answers 'what are the chances it happens at least once'.
The rules for combining events
- A AND B (independent)
- Multiply: P(A) × P(B). Both must happen, so the chance falls.
- A OR B (mutually exclusive)
- Add: P(A) + P(B). Used when they cannot both occur, like rolling a 1 or a 2.
- A OR B (can overlap)
- P(A) + P(B) − P(both), so the overlap is not counted twice.
- NOT A
- 1 − P(A). Often the easiest route into a hard question.
- At least one in n tries
- 1 − (chance of failing every time). Work out total failure, then subtract from 1.
What this assumes
Events are independent unless you say otherwise. Drawing cards without replacement is not independent, because each draw changes what is left.
Every outcome is equally likely, which holds for fair dice and coins but not for real-world events.
How to calculate a probability
Decide whether you need both things or either thing, then multiply or add accordingly.
- p
- The chance on a single attempt
- (1 − p)ⁿ
- The chance of failing every single time
- 1 −
- Everything else, which is at least one success
Work out the single-event chance. Favourable outcomes divided by total outcomes. One six out of six faces is 1/6.
For AND, multiply. Both events happening: multiply their probabilities together.
For 'at least one', flip the question. Work out the chance of it never happening, then subtract from 1. This is far easier than adding up every way it could happen.
See a worked example: the chance of at least one 6 in four rolls
- Chance of a 6
- 1/6 on each roll
- Rolls
- 4
Flip it: the chance of NOT rolling a 6 is 5/6.
Failing all four times: (5/6)⁴ = 0.4823.
So at least one 6: 1 − 0.4823 = 0.5177.
That is 51.77%, or slightly better than even. Most people guess much lower, because four tries at a 1-in-6 chance does not feel like a coin flip.
51.77%, just better than even
Frequently asked questions
Multiply for AND, when you need both things to happen. Add for OR, when either one will do and they cannot both occur.
The sanity check is direction. Needing two things should make the answer smaller, and multiplying does that. If adding gives you something above 1, you have definitely used the wrong rule.
One event has no effect on the other. Coin flips are independent: the coin has no memory of the last one.
Drawing cards without putting them back is not independent, because removing a card changes what remains. Those need conditional probability rather than simple multiplication.
Calculate the chance of it never happening, then subtract from 1. It is almost always easier than the direct route.
For at least one 6 in four rolls: failing every time is (5/6)⁴ = 0.4823, so at least one is 51.77%. Adding up 'exactly one, exactly two, exactly three, exactly four' gives the same answer with far more work.
No. For independent events the next attempt has exactly the same odds as the first, regardless of what came before.
This is the gambler's fallacy. A roulette wheel that has landed red ten times running is no more likely to land black next spin, because the wheel has no memory of the previous ten.
Probability compares successes to all outcomes: a 1 in 6 chance is 16.7%. Odds compare successes to failures: 1 to 5 against.
They describe the same thing differently, which is why betting odds and percentages never look alike. Odds of 1:1 mean a 50% probability, not 100%.
Problems people actually run into
Underestimating 'at least one'
Four rolls at a 1-in-6 chance feels like it should be well under even. It is 51.77%, slightly better than a coin flip.
This intuition failure matters outside games. A process with a 1% failure rate run a hundred times fails at least once about 63% of the time, which is why rare risks stop being rare once you repeat them enough.
Adding probabilities that can both happen
Adding only works when the events cannot occur together. The chance of rain on Saturday or Sunday, at 50% each, is not 100%.
Because both days can rain, you must subtract the overlap: 0.5 + 0.5 − 0.25 = 0.75. Any time addition produces a figure above 1, this is why.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026