🎲 Probability Calculator

1. Identify the event you want to quantify in terms of favorable outcomes and total possible outcomes.
2. For single event probability, enter the number of favorable outcomes and the total number of possible outcomes.
3. For combined events, calculate each event separately, then combine the single-event results by hand — multiply for independent events all occurring, or apply the addition rule for at least one event (see the FAQ).
4. Press Calculate to see the result as a decimal, percentage, and odds ratio.
5. Verify that your inputs make sense. Probabilities must be between 0 and 1, and total outcomes must be greater than zero.

What is the difference between independent and dependent events?

Independent events do not affect each other. Flipping a coin twice gives independent events because the first flip does not change the odds of the second. Dependent events are affected by prior outcomes, like drawing cards without replacement. This calculator assumes independence. For dependent events, you need to adjust probabilities after each step manually.

How do I calculate probability of at least one event?

It is easier to calculate the probability of none of the events occurring, then subtract from 1. For example, the probability of rolling at least one 6 in two rolls equals 1 minus the probability of no 6 in two rolls, which is 1 minus five-sixths times five-sixths, giving about 30.56 percent.

Can probability be greater than 1?

No, probability always ranges from 0 to 1, or 0 to 100 percent. If your calculation yields a value outside this range, there is an error in your inputs. The number of favorable outcomes cannot exceed the total number of possible outcomes.

How is odds different from probability?

Probability is favorable outcomes divided by total outcomes. Odds compare favorable to unfavorable outcomes. A probability of one-fourth corresponds to odds of 1 to 3, meaning one favorable outcome for every three unfavorable ones. The calculator shows both formats.

When working with probability, always clarify whether events are independent or dependent, as this fundamentally changes the calculation method. For real-world risk assessment, remember that theoretical probability assumes ideal conditions, while actual outcomes can vary due to bias, imperfect randomness, or hidden factors. In gambling and lotteries, the house edge means the true expected value is always negative over the long run, regardless of short-term wins. Use probability as a guide for decision-making, not as a guarantee of specific outcomes. This calculator runs entirely in your browser.