About the Probability Calculator
A probability calculator finds the likelihood of an event from the number of favourable outcomes against the total possible, and combines two events through union, intersection, and complement. Probability is the mathematics of uncertainty and underlies risk, insurance, genetics, and every game of chance.
The formula
P(A) = favourable outcomes / total outcomesP(A) runs from 0 (impossible) to 1 (certain). The complement P(not A) is 1 − P(A). For independent events, P(A and B) = P(A) · P(B), and P(A or B) = P(A) + P(B) − P(A and B).
How to use this calculator
- 1Enter your Favorable Outcomes. The field starts at
3, which you can overwrite. - 2Enter your Total Possible Outcomes. The field starts at
6, which you can overwrite. - 3Enter your P(B) — Second Event (%). The field starts at
40, which you can overwrite. - 4Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Favorable Outcomes | 3 |
| Total Possible Outcomes | 6 |
| P(B) — Second Event (%) | 40 |
Result
P(A) = 0.5000 (50.00%)
P(A∪B) = 0.7000
P(A∩B) = 0.2000
P(A') = 0.5000
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Independence is the assumption that does the most damage when it is wrong. Two coin flips are genuinely independent, so multiplying is valid. But the probability of two loans defaulting is not the product of their individual probabilities if both depend on the same economy — treating correlated risks as independent is precisely what went wrong in 2008.
The complement rule is the most practical shortcut in probability. Calculating the chance of "at least one" success directly means summing many cases; calculating the chance of zero successes and subtracting from 1 usually takes one line. For six dice rolls, the probability of at least one six is 1 − (5/6)⁶ ≈ 0.665.
Things worth knowing
- Probabilities of all mutually exclusive outcomes must sum to 1.
- Use the complement rule for "at least one" problems — it is nearly always faster.
- Independent means one event does not change the other's probability. Mutually exclusive means they cannot both happen. These are different things.
- Conditional probability P(A|B) can differ enormously from P(A), which is the basis of Bayes' theorem.
- Past independent results never change future odds. That belief is the gambler's fallacy.
Frequently asked questions
How do I calculate basic probability?+
Divide favourable outcomes by total possible outcomes, assuming each is equally likely. Rolling a 3 on a fair die is 1 ÷ 6 ≈ 0.167, or about 16.7 percent.
What is the difference between independent and mutually exclusive?+
Independent events do not affect each other's probability, like two coin flips. Mutually exclusive events cannot both occur, like rolling a 3 and a 5 on one die. Mutually exclusive events are never independent.
How do I find the probability of A or B?+
Add the individual probabilities and subtract the overlap: P(A) + P(B) − P(A and B). Subtracting prevents double-counting outcomes that satisfy both. For mutually exclusive events the overlap is zero.
What is the gambler's fallacy?+
The belief that independent events are "due" to correct — that after five reds, black is more likely. Each spin is independent, so the odds never change based on history.