Probability Calculator
Six Ways to Ask "How Likely Is That?"
Probability questions rarely come in just one shape. Sometimes you want the odds of a single event; sometimes you need to combine two events with "and" or "or"; sometimes the question is conditional — given that one thing happened, how likely is another? This calculator covers all of the core cases with the formula each one actually depends on, rather than a single one-size-fits-all approximation.
The Formulas
Complement: P(not A) = 1 − P(A)
And (independent): P(A and B) = P(A) × P(B)
Or (independent): P(A or B) = P(A) + P(B) − P(A) × P(B)
Or (mutually exclusive): P(A or B) = P(A) + P(B)
Conditional: P(A|B) = P(A and B) ÷ P(B)
"Independent" means the outcome of one event has no bearing on the other (two separate coin flips). "Mutually exclusive" means the two events can't both happen (rolling a 2 and rolling a 5 on the same single die roll).
Reference Probabilities
These well-known baseline probabilities are useful for sanity-checking your own inputs:
| Event | Probability |
|---|---|
| Coin lands heads | 0.5 (50%) |
| Standard die shows a 6 | 0.1667 (16.67%) |
| Drawing an ace from a 52-card deck | 0.0769 (7.69%) |
| Two independent dice both show 6 | 0.0278 (2.78%) |
Where Each Mode Applies
- Basic probability — a single lottery draw, a single die roll, a single random selection.
- Complement — "at least one" problems are often easier solved as 1 minus the probability of none happening.
- And / Or (independent) — combining separate random events, like two unrelated machines both failing this month.
- Conditional — medical testing (probability of disease given a positive test), risk assessment, and any scenario where new information changes the odds.
How to Use This Calculator
- Select the calculation type from the dropdown — Basic Probability, Complement, And, Or, or Conditional.
- Fill in the fields that appear (favorable/total outcomes, or the input probabilities P(A) and P(B), each between 0 and 1).
- Select Calculate to get the resulting probability as both a decimal and a percentage.
Related Calculations
For probabilities involving a fixed number of independent trials, see the Binomial Distribution Calculator. To convert a probability back into a required sample size, try the Sample Size Calculator.